Minimal length scale scenarios for quantum gravity

Living Reviews in Relativity

Volumn 16, Issue , 2013, Pages

  Hossenfelder, Sabine ^a  

^a NORDITA   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84873109964     PISSN: None     EISSN: 14338351     Source Type: Journal    
DOI: 10.12942/lrr-2013-2     Document Type: Review

References (321)

1. Abel, S. and Santiago, J., "Constraining the string scale: from Planck to weak and back again", J. Phys. G: Nucl. Part. Phys., 30, R83-R111 (2004). [DOI], [arXiv:hep-ph/0404237]. (Cited on page 23.)
2. Adler, R.J., Chen, P. and Santiago, D.I., "The Generalized Uncertainty Principle and Black Hole Remnants", Gen. Relativ. Gravit., 33, 2101-2108 (2001). [DOI], [arXiv:gr-qc/0106080 [gr-qc]. (Cited on page 64.)
3. Adler, R.J. and Santiago, D.I., "On gravity and the uncertainty principle", Mod. Phys. Lett. A, 14, 1371 (1999). [DOI], [arXiv:gr-qc/9904026]. (Cited on pages 10, 13, 15, and 16.)
4. Agostini, A., Amelino-Camelia, G., Arzano, M., Marcianò, A. and Altair Tacchi, R., "Generalizing the Noether theorem for Hopf-algebra spacetime symmetries", Mod. Phys. Lett. A, 22, 1779-1786 (2007). [DOI], [ADS], [arXiv:hep-th/0607221 [hep-th]. (Cited on page 60.)
5. Ahluwalia-Khalilova, D.V., "Operational indistinguishability of doubly special relativities from special relativity", arXiv, e-print, (2002). [arXiv:gr-qc/0212128 [gr-qc]. (Cited on page 58.)
6. Ali, A.F., "Minimal Length in Quantum Gravity, Equivalence Principle and Holographic Entropy Bound", Class. Quantum Grav., 28, 065013 (2011). [DOI], [arXiv:1101.4181 [hep-th]. (Cited on page 62.)
7. Ali, A.F., Das, S. and Vagenas, E.C., "Discreteness of Space from the Generalized Uncertainty Principle", Phys. Lett. B, 678, 497-499 (2009). [DOI], [arXiv:0906.5396 [hep-th]. (Cited on page 59.)
8. Ali, A.F., Das, S. and Vagenas, E.C., "A proposal for testing quantum gravity in the lab", Phys. Rev. D, 84, 044013 (2011). [DOI], [arXiv:1107.3164 [hep-th]. (Cited on page 59.)
9. Amati, D., Ciafaloni, M. and Veneziano, G., "Superstring Collisions at Planckian Energies", Phys. Lett. B, 197, 81 (1987). [DOI]. (Cited on pages 10 and 25.)
10. Amati, D., Ciafaloni, M. and Veneziano, G., "Classical and Quantum Gravity Effects from Planckian Energy Superstring Collisions", Int. J. Mod. Phys. A, 3, 1615-1661 (1988). [DOI]. (Cited on pages 10 and 25.)
11. Amati, D., Ciafaloni, M. and Veneziano, G., "Higher order gravitational deflection and soft bremsstrahlung in Planckian energy superstring collisions", Nucl. Phys. B, 347, 550-580 (1990). [DOI]. (Cited on pages 10 and 25.)
12. Amati, D., Ciafaloni, M. and Veneziano, G., "Towards an S-matrix description of gravitational collapse", J. High Energy Phys., 2008(02), 049 (2008). [DOI], [arXiv:0712.1209 [hep-th]. (Cited on page 25.)
13. Ambjorn, J., Jurkiewicz, J. and Loll, R., "Causal dynamical triangulations and the quest for quantum gravity", in Murugan, J., Weltman, A. and Ellis, G.F.R., eds., Foundations of Space and Time: Reflections on Quantum Gravity, pp. 321-337, (Cambridge University Press, Cambridge; New York, 2012). [arXiv:1004.0352 [hep-th]. (Cited on page 68.)
14. Amelino-Camelia, G., "Testable scenario for relativity with minimum length", Phys. Lett. B, 510, 255-263 (2001). [DOI], [arXiv:hep-th/0012238 [hep-th]. (Cited on page 46.)
15. Amelino-Camelia, G., "Doubly special relativity", Nature, 418, 34-35 (2002). [DOI], [arXiv:grqc/ 0207049 [gr-qc]. (Cited on page 46.)
16. Amelino-Camelia, G., "Doubly special relativity: First results and key open problems", Int. J. Mod. Phys. D, 11, 1643 (2002). [DOI], [arXiv:gr-qc/0210063 [gr-qc]. (Cited on page 58.)
17. Amelino-Camelia, G., "Kinematical solution of the UHE-cosmic-ray puzzle without a preferred class of inertial observers", Int. J. Mod. Phys. D, 12, 1211-1226 (2003). [DOI], [arXiv:astro-ph/0209232 [astro-ph]. (Cited on page 62.)
18. Amelino-Camelia, G., "Planck-scale Lorentz-symmetry test theories", arXiv, e-print, (2004). [arXiv:astro-ph/0410076 [astro-ph]. (Cited on page 61.)
19. Amelino-Camelia, G., "Quantum Gravity Phenomenology", arXiv, e-print, (2008). [arXiv:0806.0339 [gr-qc]. (Cited on pages 61, 62, 66, and 67.)
20. Amelino-Camelia, G., "Doubly-Special Relativity: Facts, Myths and Some Key Open Issues", Symmetry, 2, 230-271 (2010). [DOI], [arXiv:1003.3942 [gr-qc]. (Cited on pages 61, 62, and 67.)
21. Amelino-Camelia, G., "On the fate of Lorentz symmetry in relative-locality momentum spaces", Phys. Rev. D, 85, 084034 (2012). [DOI], [arXiv:1110.5081 [hep-th]. (Cited on pages 48, 57, 58, and 62.)
22. Amelino-Camelia, G., Arzano, M., Ling, Y. and Mandanici, G., "Black-hole thermodynamics with modified dispersion relations and generalized uncertainty principles", Class. Quantum Grav., 23, 2585-2606 (2006). [DOI], [arXiv:gr-qc/0506110 [gr-qc]. (Cited on page 64.)
23. Amelino-Camelia, G., Freidel, L., Kowalski-Glikman, J. and Smolin, L., "The principle of relative locality", Phys. Rev. D, 84, 084010 (2011). [DOI], [arXiv:1101.0931 [hep-th]. (Cited on pages 48, 57, 58, and 62.)
24. Amelino-Camelia, G., Freidel, L., Kowalski-Glikman, J. and Smolin, L., "Relative locality and the soccer ball problem", Phys. Rev. D, 84, 087702 (2011). [DOI], [arXiv:1104.2019 [hep-th]. (Cited on page 56.)
25. Amelino-Camelia, G., Lukierski, J. and Nowicki, A., "Distance measurement and κ-deformed propagation of light and heavy probes", Int. J. Mod. Phys. A, 14, 4575-4588 (1999). [DOI], [arXiv:grqc/ 9903066 [gr-qc]. (Cited on page 48.)
26. Amelino-Camelia, G. and Majid, S., "Waves on noncommutative space-time and gamma-ray bursts", Int. J. Mod. Phys. A, 15, 4301-4324 (2000). [DOI], [arXiv:hep-th/9907110 [hep-th]. (Cited on pages 48, 58, 62, and 67.)
27. Amelino-Camelia, G., Matassa, M., Mercati, F. and Rosati, G., "Taming Nonlocality in Theories with Planck-Scale Deformed Lorentz Symmetry", Phys. Rev. Lett., 106, 071301 (2011). [DOI], [arXiv:1006.2126 [gr-qc]. (Cited on pages 48, 57, 58, and 62.)
28. Amelino-Camelia, G., Procaccini, A. and Arzano, M., "A glimpse at the flat-spacetime limit of quantum gravity using the Bekenstein argument in reverse", Int. J. Mod. Phys. D, 13, 2337-2343 (2004). [DOI], [arXiv:hep-th/0506182 [hep-th]. (Cited on page 64.)
29. Amelino-Camelia, G., Smolin, L. and Starodubtsev, A., "Quantum symmetry, the cosmological constant and Planck scale phenomenology", Class. Quantum Grav., 21, 3095-3110 (2004). [DOI], [arXiv:hep-th/0306134 [hep-th]. (Cited on page 66.)
30. Anber, M.M. and Donoghue, J.F., "On the running of the gravitational constant", Phys. Rev. D, 85, 104016 (2012). [DOI], [arXiv:1111.2875 [hep-th]. (Cited on page 41.)
31. Arzano, M., "Anatomy of a deformed symmetry: Field quantization on curved momentum space", Phys. Rev. D, 83, 025025 (2011). [DOI], [arXiv:1009.1097 [hep-th]. (Cited on page 60.)
32. Arzano, M. and Kowalski-Glikman, J., "Kinematics of a relativistic particle with de Sitter momentum space", Class. Quantum Grav., 28, 105009 (2011). [DOI], [arXiv:1008.2962 [hep-th]. (Cited on page 65.)
33. Arzano, M., Kowalski-Glikman, J. and Walkus, A., "Lorentz invariant field theory on κ-Minkowski space", Class. Quantum Grav., 27, 025012 (2010). [DOI], [arXiv:0908.1974 [hep-th]. (Cited on page 60.)
34. Arzano, M. and Marciano, A., "Fock space, quantum fields and κ-Poincaré symmetries", Phys. Rev. D, 76, 125005 (2007). [DOI], [arXiv:0707.1329 [hep-th]. (Cited on page 60.)
35. Arzano, M. and Marcianò, A., "Symplectic geometry and Noether charges for Hopf algebra spacetime symmetries", Phys. Rev. D, 75, 081701 (2007). [DOI], [arXiv:hep-th/0701268 [hep-th]. (Cited on page 60.)
36. Ashoorioon, A., Hovdebo, J.L. and Mann, R.B., "Running of the spectral index and violation of the consistency relation between tensor and scalar spectra from trans-Planckian physics", Nucl. Phys. B, 727, 63-76 (2005). [DOI], [arXiv:gr-qc/0504135 [gr-qc]. (Cited on page 67.)
37. Ashoorioon, A., Kempf, A. and Mann, R.B., "Minimum length cutoff in inflation and uniqueness of the action", Phys. Rev. D, 71, 023503 (2005). [DOI], [arXiv:astro-ph/0410139 [astro-ph]. (Cited on page 67.)
38. Ashoorioon, A. and Mann, R.B., "On the tensor/scalar ratio in inflation with UV cut off", Nucl. Phys. B, 716, 261-279 (2005). [DOI], [arXiv:gr-qc/0411056 [gr-qc]. (Cited on page 67.)
39. Ashtekar, A., "New Variables for Classical and Quantum Gravity", Phys. Rev. Lett., 57, 2244-2247 (1986). [DOI]. (Cited on page 32.)
40. Ashtekar, A., Bojowald, M. and Lewandowski, J., "Mathematical structure of loop quantum cosmology", Adv. Theor. Math. Phys., 7, 233-268 (2003). [arXiv:gr-qc/0304074]. (Cited on pages 34 and 35.)
41. Ashtekar, A. and Lewandowski, J., "Quantum theory of geometry. II: Volume operators", Adv. Theor. Math. Phys., 1, 388-429 (1998). [arXiv:gr-qc/9711031]. (Cited on page 34.)
42. Ashtekar, A. and Lewandowski, J., "Background independent quantum gravity: a status report", Class. Quantum Grav., 21, R53-R152 (2004). [DOI], [arXiv:gr-qc/0404018]. (Cited on page 32.)
43. Ashtekar, A., Pawlowski, T., Singh, P. and Vandersloot, K., "Loop quantum cosmology of κ = 1 FRW models", Phys. Rev. D, 75, 024035 (2007). [DOI], [arXiv:gr-qc/0612104]. (Cited on page 36.)
44. Ashtekar, A. and Singh, P., "Loop Quantum Cosmology: A Status Report", Class. Quantum Grav., 28, 213001 (2011). [DOI], [arXiv:1108.0893 [gr-qc]. (Cited on pages 34 and 36.)
45. Bachas, C.P., "Lectures on D-branes", arXiv, e-print, (1998). [arXiv:hep-th/9806199]. (Cited on pages 27 and 30.)
46. Bachmann, S. and Kempf, A., "The Transplanckian Question and the Casimir Effect", arXiv, e-print, (2005). [arXiv:gr-qc/0504076 [gr-qc]. (Cited on page 59.)
47. Banks, T., "A critique of pure string theory: Heterodox opinions of diverse dimensions", arXiv, e-print, (2003). [arXiv:hep-th/0306074]. (Cited on page 25.)
48. Banks, T. and Fischler, W., "A Model for High Energy Scattering in Quantum Gravity", arXiv, e-print, (1999). [arXiv:hep-th/9906038]. (Cited on page 25.)
49. Barceló, C., Liberati, S. and Visser, M., "Analogue Gravity", Living Rev. Relativity, 14, lrr-2011-03 (2011). [arXiv:gr-qc/0505065 [gr-qc]. URL (accessed 20 January 2012): http://www.livingreviews.org/lrr-2011-3. (Cited on page 44.)
50. Barrau, A., Cailleteau, T., Cao, X., Diaz-Polo, J. and Grain, J., "Probing Loop Quantum Gravity with Evaporating Black Holes", Phys. Rev. Lett., 107, 251301 (2011). [DOI], [arXiv:1109.4239 [grqc]. (Cited on page 66.)
51. Basu, S. and Mattingly, D., "Asymptotic Safety, Asymptotic Darkness, and the hoop conjecture in the extreme UV", Phys. Rev. D, 82, 124017 (2010). [DOI], [arXiv:1006.0718 [hep-th]. (Cited on pages 39 and 68.)
52. Battisti, M.V. and Montani, G., "The Big-Bang singularity in the framework of a Generalized Uncertainty Principle", Phys. Lett. B, 656, 96-101 (2007). [DOI], [arXiv:gr-qc/0703025 [gr-qc]. (Cited on page 64.)
53. Battisti, M.V. and Montani, G., "Quantum dynamics of the Taub universe in a generalized uncertainty principle framework", Phys. Rev. D, 77, 023518 (2008). [DOI], [arXiv:0707.2726 [gr-qc]. (Cited on page 64.)
54. Bina, A., Jalalzadeh, S. and Moslehi, A., "Quantum Black Hole in the Generalized Uncertainty Principle Framework", Phys. Rev. D, 81, 023528 (2010). [DOI], [arXiv:1001.0861 [gr-qc]. (Cited on page 64.)
55. Blaut, A., Daszkiewicz, M., Kowalski-Glikman, J. and Nowak, S., "Phase spaces of doubly special relativity", Phys. Lett. B, 582, 82-85 (2004). [DOI], [arXiv:hep-th/0312045 [hep-th]. (Cited on page 53.)
56. Bojowald, M., "Absence of singularity in loop quantum cosmology", Phys. Rev. Lett., 86, 5227-5230 (2001). [DOI], [arXiv:gr-qc/0102069]. (Cited on page 36.)
57. Bojowald, M., "Dynamical coherent states and physical solutions of quantum cosmological bounces", Phys. Rev. D, 75, 123512 (2007). [DOI], [arXiv:gr-qc/0703144]. (Cited on pages 34 and 36.)
58. Bojowald, M., "Loop Quantum Cosmology", Living Rev. Relativity, 11, lrr-2008-4 (2008). URL (accessed 20 January 2012): http://www.livingreviews.org/lrr-2008-4. (Cited on pages 34 and 36.)
59. Bojowald, M., "Quantum Geometry and Quantum Dynamics at the Planck Scale", in Kowalski-Glikman, J., Durka, R. and Szczachor, M., eds., The Planck Scale, Proceedings of the XXV Max Born Symposium, Wroclaw, Poland, 29 June-03 July 2009, AIP Conference Proceedings, 1196, pp. 62-71, (American Institute of Physics, Melville, NY, 2009). [DOI], [arXiv:0910.2936 [gr-qc]. (Cited on page 66.)
60. Bojowald, M. and Kempf, A., "Generalized uncertainty principles and localization of a particle in discrete space", Phys. Rev. D, 86, 085017 (2012). [DOI], [arXiv:1112.0994 [hep-th]. (Cited on pages 44 and 66.)
61. Bolen, B. and Cavaglia, M., "(Anti-)de Sitter black hole thermodynamics and the generalized uncertainty principle", Gen. Relativ. Gravit., 37, 1255-1262 (2005). [DOI], [arXiv:gr-qc/0411086 [gr-qc]. (Cited on page 64.)
62. Bombelli, L., Henson, J. and Sorkin, R.D., "Discreteness without symmetry breaking: A Theorem", Mod. Phys. Lett. A, 24, 2579-2587 (2009). [DOI], [arXiv:gr-qc/0605006 [gr-qc]. (Cited on page 44.)
63. Bombelli, L. and Meyer, D.A., "The origin of Lorentzian geometry", Phys. Lett. A, 141, 226-228 (1989). [DOI]. (Cited on page 44.)
64. Born, M., "A suggestion for unifying quantum theory and relativity", Proc. R. Soc. London, Ser. A, 165, 291-303 (1938). [DOI]. (Cited on page 48.)
65. Bouaziz, D. and Bawin, M., "Regularization of the Singular Inverse Square Potential in Quantum Mechanics with a Minimal length", Phys. Rev. A, 76, 032112 (2007). [DOI], [arXiv:0711.0599 [quantph]. (Cited on page 59.)
66. Bouaziz, D. and Bawin, M., "Singular inverse square potential in arbitrary dimensions with a minimal length: Application to the motion of a dipole in a cosmic string background", Phys. Rev. A, 78, 032110 (2008). [DOI], [arXiv:1009.0930 [quant-ph]. (Cited on page 59.)
67. Bouaziz, D. and Ferkous, N., "Hydrogen atom in momentum space with a minimal length", Phys. Rev. A, 82, 022105 (2010). [DOI], [arXiv:1009.0935 [quant-ph]. (Cited on page 59.)
68. Brandenberger, R.H. and Ho, P.-M., "Noncommutative space-time, stringy space-time uncertainty principle, and density fluctuations", Phys. Rev. D, 66, 023517 (2002). [DOI], [arXiv:hep-th/0203119 [hep-th]. (Cited on pages 65 and 67.)
69. Brau, F., "Minimal length uncertainty relation and hydrogen atom", J. Phys. A: Math. Gen., 32, 7691-7696 (1999). [DOI], [arXiv:quant-ph/9905033 [quant-ph]. (Cited on page 59.)
70. Bronstein, M., "Quantentheorie schwacher Gravitationsfelder", Phys. Z. Sowjetunion, 9, 140-157 (1936). (Cited on pages 6 and 7.)
71. Bruno, N.R., Amelino-Camelia, G. and Kowalski-Glikman, J., "Deformed boost transformations that saturate at the Planck scale", Phys. Lett. B, 522, 133-138 (2001). [DOI], [arXiv:hep-th/0107039 [hep-th]. (Cited on page 62.)
72. Calmet, X., Graesser, M. and Hsu, S.D.H., "Minimum length from quantum mechanics and general relativity", Phys. Rev. Lett., 93, 211101 (2004). [DOI], [arXiv:hep-th/0405033]. (Cited on page 19.)
73. Calmet, X., Graesser, M.L. and Hsu, S.D.H., "Minimum length from first principles", Int. J. Mod. Phys. D, 14, 2195-2200 (2005). [DOI], [arXiv:hep-th/0505144]. (Cited on page 19.)
74. Calmet, X., Hossenfelder, S. and Percacci, R., "Deformed Special Relativity from Asymptotically Safe Gravity", Phys. Rev. D, 82, 124024 (2010). [DOI], [arXiv:1008.3345 [gr-qc]. (Cited on pages 39, 41, 47, 57, and 66.)
75. Camacho, A., "Generalized uncertainty principle and quantum electrodynamics", Gen. Relativ. Gravit., 35, 1153-1160 (2003). [DOI], [arXiv:gr-qc/0303061 [gr-qc]. (Cited on page 60.)
76. Campo, D., "Problems with models of a fundamental length", arXiv, e-print, (2010). [arXiv:1004.5324 [gr-qc]. (Cited on page 64.)
77. Carmona, J.M., Cortes, J.L., Indurain, J. and Mazon, D., "Quantum Noncanonical Field Theory: Symmetries and Interaction", Phys. Rev. D, 80, 105014 (2009). [DOI], [arXiv:0905.1901 [hep-th]. (Cited on page 60.)
78. Carmona, J.M., Cortes, J.L. and Mazon, D., "Asymptotic approach to Special Relativity compatible with a relativistic principle", Phys. Rev. D, 82, 085012 (2010). [DOI], [arXiv:1007.3190 [gr-qc]. (Cited on page 62.)
79. Carmona, J.M., Cortes, J.L., Mazon, D. and Mercati, F., "About Locality and the Relativity Principle Beyond Special Relativity", Phys. Rev. D, 84, 085010 (2011). [DOI], [arXiv:1107.0939 [hep-th]. (Cited on pages 58 and 62.)
80. Carr, B., Modesto, L. and Prémont-Schwarz, I., "Generalized Uncertainty Principle and Self-dual Black Holes", arXiv, e-print, (2011). [arXiv:1107.0708 [gr-qc]. (Cited on page 64.)
81. Cavaglia, M. and Das, S., "How classical are TeV scale black holes?", Class. Quantum Grav., 21, 4511-4522 (2004). [DOI], [arXiv:hep-th/0404050 [hep-th]. (Cited on page 61.)
82. Chandra, N. and Chatterjee, S., "Thermodynamics of Ideal Gas in Doubly Special Relativity", Phys. Rev. D, 85, 045012 (2012). [DOI], [arXiv:1108.0896 [gr-qc]. (Cited on page 63.)
83. Chang, L.N., Lewis, Z., Minic, D. and Takeuchi, T., "On the Minimal Length Uncertainty Relation and the Foundations of String Theory", Adv. High Energy Phys., 2011, 493514 (2011). [DOI], [arXiv:1106.0068 [hep-th]. (Cited on page 59.)
84. Chang, L.N., Minic, D., Okamura, N. and Takeuchi, T., "The Effect of the minimal length uncertainty relation on the density of states and the cosmological constant problem", Phys. Rev. D, 65, 125028 (2002). [DOI], [arXiv:hep-th/0201017 [hep-th]. (Cited on page 62.)
85. Chang, L.N., Minic, D., Okamura, N. and Takeuchi, T., "Exact solution of the harmonic oscillator in arbitrary dimensions with minimal length uncertainty relations", Phys. Rev. D, 65, 125027 (2002). [DOI], [arXiv:hep-th/0111181 [hep-th]. (Cited on page 59.)
86. Chang, L.N., Minic, D. and Takeuchi, T., "Quantum Gravity, Dynamical Energy-Momentum Space and Vacuum Energy", Mod. Phys. Lett. A, 25, 2947-2954 (2010). [DOI], [arXiv:1004.4220 [hep-th]. (Cited on page 57.)
87. Chen, P. and Adler, R.J., "Black hole remnants and dark matter", Nucl. Phys. B (Proc. Suppl.), 124, 103-106 (2003). [DOI], [arXiv:gr-qc/0205106 [gr-qc]. (Cited on page 64.)
88. Chialva, D., "Enhanced CMBR non-Gaussianities from Lorentz violation", J. Cosmol. Astropart. Phys., 2012(01), 037 (2012). [DOI], [arXiv:1106.0040 [hep-th]. (Cited on page 67.)
89. Chialva, D., "Signatures of very high energy physics in the squeezed limit of the bispectrum", J. Cosmol. Astropart. Phys., 2012(10), 037 (2012). [DOI], [arXiv:1108.4203 [astro-ph.CO]. (Cited on page 67.)
90. Ciafaloni, M. and Colferai, D., "Quantum Tunneling and Unitarity Features of an S-matrix for Gravitational Collapse", J. High Energy Phys., 2009(12), 062 (2009). [DOI], [arXiv:0909.4523 [hepth]. (Cited on page 25.)
91. Coleman, S.R., Preskill, J. and Wilczek, F., "Quantum hair on black holes", Nucl. Phys. B, 378, 175-246 (1992). [DOI], [arXiv:hep-th/9201059]. (Cited on page 18.)
92. Cunliff, C., "Conformal fluctuations do not establish a minimum length", arXiv, e-print, (2012). [arXiv:1201.2247 [gr-qc]. (Cited on page 37.)
93. Dadic, I., Jonke, L. and Meljanac, S., "Harmonic oscillator with minimal length uncertainty relations and ladder operators", Phys. Rev. D, 67, 087701 (2003). [DOI], [arXiv:hep-th/0210264 [hep-th]. (Cited on page 59.)
94. Das, S., Ghosh, S. and Roychowdhury, D., "Relativistic Thermodynamics with an Invariant Energy Scale", Phys. Rev. D, 80, 125036 (2009). [DOI], [arXiv:0908.0413 [hep-th]. (Cited on page 63.)
95. Das, S. and Mann, R.B., "Planck scale effects on some low energy quantum phenomena", Phys. Lett. B, 704, 596-599 (2011). [DOI], [arXiv:1109.3258 [hep-th]. (Cited on page 59.)
96. Das, S. and Vagenas, E.C., "Universality of Quantum Gravity Corrections", Phys. Rev. Lett., 101, 221301 (2008). [DOI], [arXiv:0810.5333 [hep-th]. (Cited on page 59.)
97. Das, S. and Vagenas, E.C., "Phenomenological Implications of the Generalized Uncertainty Principle", Can. J. Phys., 87, 233-240 (2009). [DOI], [arXiv:0901.1768 [hep-th]. (Cited on page 59.)
98. Das, S., Vagenas, E.C. and Ali, A.F., "Discreteness of Space from GUP II: Relativistic Wave Equations", Phys. Lett. B, 690, 407-412 (2010). [DOI], [arXiv:1005.3368 [hep-th]. (Cited on page 60.)
99. Daszkiewicz, M., Imilkowska, K. and Kowalski-Glikman, J., "Velocity of particles in doubly special relativity", Phys. Lett. A, 323, 345-350 (2004). [DOI], [arXiv:hep-th/0304027 [hep-th]. (Cited on pages 58 and 62.)
100. Dehghani, M., "Corrected black hole's thermodynamics and tunneling radiation with generalized uncertainty principle and modified dispersion relation", Int. J. Theor. Phys., 50, 618-624 (2011). [DOI]. (Cited on page 64.)
101. Doplicher, S., Fredenhagen, K. and Roberts, J.E., "The quantum structure of space-time at the Planck scale and quantum fields", Commun. Math. Phys., 172, 187-220 (1995). [DOI], [arXiv:hepth/ 0303037]. (Cited on pages 21 and 22.)
102. Dorsch, G. and Nogueira, J.A., "Maximally Localized States in Quantum Mechanics with a Modified Commutation Relation to All Orders", Int. J. Mod. Phys. A, 27, 1250113 (2012). [DOI], [arXiv:1106.2737 [hep-th]. (Cited on page 59.)
103. Douglas, M.R., Kabat, D.N., Pouliot, P. and Shenker, S.H., "D-branes and short distances in string theory", Nucl. Phys. B, 485, 85-127 (1997). [DOI], [arXiv:hep-th/9608024]. (Cited on pages 27 and 30.)
104. Douglas, M.R. and Nekrasov, N.A., "Noncommutative field theory", Rev. Mod. Phys., 73, 977-1029 (2001). [DOI], [arXiv:hep-th/0106048 [hep-th]. (Cited on pages 41 and 60.)
105. Dvali, G., Folkerts, S. and Germani, C., "Physics of Trans-Planckian Gravity", Phys. Rev. D, 84, 024039 (2011). [DOI], [arXiv:1006.0984 [hep-th]. (Cited on pages 45 and 47.)
106. Dvali, G. and Gomez, C., "Self-Completeness of Einstein Gravity", arXiv, e-print, (2010). [arXiv:1005.3497 [hep-th]. (Cited on pages 45 and 47.)
107. Eardley, D.M. and Giddings, S.B., "Classical black hole production in high-energy collisions", Phys. Rev. D, 66, 044011 (2002). [DOI], [arXiv:gr-qc/0201034]. (Cited on page 13.)
108. Falls, K., Litim, D.F. and Raghuraman, A., "Black holes and asymptotically safe gravity", Int. J. Mod. Phys. A, 27, 1250019 (2012). [DOI], [arXiv:1002.0260 [hep-th]. (Cited on page 39.)
109. Fityo, T.V., "Statistical physics in deformed spaces with minimal length", Phys. Lett. A, 372, 5872-5877 (2008). [DOI]. (Cited on page 62.)
110. Flint, H.T., "Relativity and the quantum theory", Proc. R. Soc. London, Ser. A, 117, 630-637 (1928). [DOI]. (Cited on page 6.)
111. Fontanini, M., Spallucci, E. and Padmanabhan, T., "Zero-point length from string fluctuations", Phys. Lett. B, 633, 627-630 (2006). [DOI], [arXiv:hep-th/0509090]. (Cited on page 31.)
112. Frassino, A.M. and Panella, O., "The Casimir Effect in Minimal Length Theories Based on a Generalized Uncertainity Principle", Phys. Rev. D, 85, 045030 (2012). [DOI], [arXiv:1112.2924 [hep-th]. (Cited on page 59.)
113. Freidel, L., Kowalski-Glikman, J. and Nowak, S., "Field theory on κ-Minkowski space revisited: Noether charges and breaking of Lorentz symmetry", Int. J. Mod. Phys. A, 23, 2687-2718 (2008). [DOI], [arXiv:0706.3658 [hep-th]. (Cited on page 60.)
114. Freidel, L., Kowalski-Glikman, J. and Smolin, L., "2+1 gravity and doubly special relativity", Phys. Rev. D, 69, 044001 (2004). [DOI], [arXiv:hep-th/0307085 [hep-th]. (Cited on page 66.)
115. Galán, P. and Mena Marugán, G.A., "Quantum time uncertainty in a gravity's rainbow formalism", Phys. Rev. D, 70, 124003 (2004). [DOI], [arXiv:gr-qc/0411089 [gr-qc]. (Cited on page 65.)
116. Galán, P. and Mena Marugán, G.A., "Length uncertainty in a gravity's rainbow formalism", Phys. Rev. D, 72, 044019 (2005). [DOI], [arXiv:gr-qc/0507098 [gr-qc]. (Cited on page 65.)
117. Galán, P. and Mena Marugán, G.A., "Entropy and temperature of black holes in a gravity's rainbow", Phys. Rev. D, 74, 044035 (2006). [DOI], [arXiv:gr-qc/0608061 [gr-qc]. (Cited on page 65.)
118. Gambini, R. and Pullin, J., A First Course in Loop Quantum Gravity, (Oxford University Press, Oxford; New York, 2011). [Google Books]. (Cited on pages 32 and 34.)
119. Garattini, R., "Modified Dispersion Relations: from Black-Hole Entropy to the Cosmological Constant", Int. J. Mod. Phys.: Conf. Ser., 14, 326-336 (2012). [DOI], [arXiv:1112.1630 [gr-qc]. (Cited on page 64.)
120. Garay, L.J., "Quantum gravity and minimum length", Int. J. Mod. Phys. A, 10, 145-166 (1995). [DOI], [arXiv:gr-qc/9403008 [gr-qc]. (Cited on pages 44 and 70.)
121. Garay, L.J., "Space-time foam as a quantum thermal bath", Phys. Rev. Lett., 80, 2508-2511 (1998). [DOI], [arXiv:gr-qc/9801024 [gr-qc]. (Cited on page 65.)
122. Garay, L.J., "Thermal properties of space-time foam", Phys. Rev. D, 58, 124015 (1998). [DOI], [arXiv:gr-qc/9806047 [gr-qc]. (Cited on page 65.)
123. Ghosh, S., "A Lagrangian for DSR Particle and the Role of Noncommutativity", Phys. Rev. D, 74, 084019 (2006). [DOI], [arXiv:hep-th/0608206 [hep-th]. (Cited on page 65.)
124. Ghosh, S., "Generalized Uncertainty Principle and Klein Paradox", arXiv, e-print, (2012). [arXiv:1202.1962 [hep-th]. (Cited on page 59.)
125. Ghosh, S. and Roy, P., "'Stringy' Coherent States Inspired By Generalized Uncertainty Principle", Phys. Lett. B, 711, 423-427 (2012). [DOI], [arXiv:1110.5136 [hep-th]. (Cited on page 59.)
126. Giddings, S.B., "Locality in quantum gravity and string theory", Phys. Rev. D, 74, 106006 (2006). [DOI], [arXiv:hep-th/0604072]. (Cited on page 44.)
127. Giddings, S.B., Gross, D.J. and Maharana, A., "Gravitational effects in ultrahigh-energy string scattering", Phys. Rev. D, 77, 046001 (2008). [DOI], [arXiv:0705.1816 [hep-th]. (Cited on page 25.)
128. Giddings, S.B. and Lippert, M., "Precursors, black holes, and a locality bound", Phys. Rev. D, 65, 024006 (2002). [DOI], [arXiv:hep-th/0103231]. (Cited on page 44.)
129. Giddings, S.B. and Lippert, M., "The information paradox and the locality bound", Phys. Rev. D, 69, 124019 (2004). [DOI], [arXiv:hep-th/0402073]. (Cited on page 44.)
130. Giddings, S.B., Schmidt-Sommerfeld, M. and Andersen, J.R., "High energy scattering in gravity and supergravity", Phys. Rev. D, 82, 104022 (2010). [DOI], [arXiv:1005.5408 [hep-th]. (Cited on page 25.)
131. Giddings, S.B. and Thomas, S.D., "High energy colliders as black hole factories: The end of short distance physics", Phys. Rev. D, 65, 056010 (2002). [DOI], [arXiv:hep-ph/0106219]. (Cited on page 25.)
132. Girelli, F., Konopka, T., Kowalski-Glikman, J. and Livine, E.R., "The free particle in deformed special relativity", Phys. Rev. D, 73, 045009 (2006). [DOI], [arXiv:hep-th/0512107 [hep-th]. (Cited on pages 54, 55, and 65.)
133. Girelli, F., Liberati, S., Percacci, R. and Rahmede, C., "Modified Dispersion Relations from the Renormalization Group of Gravity", Class. Quantum Grav., 24, 3995-4008 (2007). [DOI], [arXiv:grqc/ 0607030 [gr-qc]. (Cited on page 66.)
134. Girelli, F. and Livine, E.R., "Physics of Deformed Special Relativity: Relativity Principle revisited", arXiv, e-print, (2004). [arXiv:gr-qc/0412004 [gr-qc]. (Cited on page 56.)
135. Girelli, F. and Livine, E.R., "Non-Commutativity of Effective Space-Time Coordinates and the Minimal Length", arXiv, e-print, (2007). [arXiv:0708.3813 [hep-th]. (Cited on page 52.)
136. Girelli, F. and Livine, E.R., "Special relativity as a non commutative geometry: Lessons for deformed special relativity", Phys. Rev. D, 81, 085041 (2010). [DOI], [arXiv:gr-qc/0407098 [gr-qc]. (Cited on page 57.)
137. Gopakumar, R., Minwalla, S. and Strominger, A., "Noncommutative solitons", J. High Energy Phys., 2000(05), 020 (2000). [DOI], [arXiv:hep-th/0003160 [hep-th]. (Cited on pages 43 and 44.)
138. Gorelik, G.E., "Matvei Bronstein and quantum gravity: 70th anniversary of the unsolved problem", Phys. Usp., 48, 1039-1053 (2005). [DOI]. (Cited on page 6.)
139. Greensite, J., "Is there a minimum length in D = 4 lattice quantum gravity?", Phys. Lett. B, 255, 375-380 (1991). [DOI]. (Cited on page 44.)
140. Gross, D.J. and Mende, P.F., "String theory beyond the Planck scale", Nucl. Phys. B, 303, 407-454 (1988). [DOI]. (Cited on pages 10 and 24.)
141. Hagar, A., "Length Matters: The History and the Philosophy of the Notion of Fundamental Length in Modern Physics", in preparation, (2012). Online version (accessed 17 December 2012): http://mypage.iu.edu/~hagara/LMBOOK.pdf. (Cited on page 10.)
142. Harbach, U. and Hossenfelder, S., "The Casimir effect in the presence of a minimal length", Phys. Lett. B, 632, 379-383 (2006). [DOI], [arXiv:hep-th/0502142 [hep-th]. (Cited on page 59.)
143. Harbach, U., Hossenfelder, S., Bleicher, M. and Stoecker, H., "Probing the minimal length scale by precision tests of the muon g-2", Phys. Lett. B, 584, 109-113 (2004). [DOI], [arXiv:hep-ph/0308138 [hep-ph]. (Cited on page 59.)
144. Hassan, S.F. and Sloth, M.S., "Trans-Planckian effects in inflationary cosmology and the modified uncertainty principle", Nucl. Phys. B, 674, 434-458 (2003). [DOI], [arXiv:hep-th/0204110 [hep-th]. (Cited on page 9.)
145. Hawking, S.W., "Particle creation by black holes", Commun. Math. Phys., 43, 199-220 (1975). [DOI]. (Cited on page 9.)
146. Heisenberg, W., The Physical Principles of the Quantum Theory, (University of Chicago Press, Chicago, 1930). [Google Books]. (Cited on page 11.)
147. Heisenberg, W., "Zur Theorie der 'Schauer' in der Höhenstrahlung", Z. Phys., 101, 533-540 (1936). [DOI]. (Cited on page 7.)
148. Heisenberg, W., "Über die in der Theorie der Elementarteilchen auftretende universelle Länge", Ann. Phys. (Leipzig), 32, 20-33 (1938). [DOI]. (Cited on pages 7 and 8.)
149. Heisenberg, W., "Bericht über die allgemeinen Eigenschaften der Elementarteilchen / Report on the General Properties of Elementary Particles", in Blum, W., Dürr, H.-P. and Rechenberg, H., eds., Werner Heisenberg: Gesammelte Werke. Collected Works, Series B, pp. 346-358, (Springer, Berlin; New York, 1984). (Cited on page 8.)
150. Heisenberg, W., "[247] Heisenberg an Peierls, 1930", in von Meyenn, K., ed., Wissenschaftlicher Briefwechsel mit Bohr, Einstein, Heisenberg u.a., Bd. II: 1930-1939, Sources in the History of Mathematics and Physical Sciences, 6, pp. 15-18, (Springer, Berlin; New York, 1985). [Google Books]. (Cited on page 8.)
151. Hinchliffe, I., Kersting, N. and Ma, Y.L., "Review of the phenomenology of noncommutative geometry", Int. J. Mod. Phys. A, 19, 179-204 (2004). [DOI], [arXiv:hep-ph/0205040 [hep-ph]. (Cited on pages 41 and 60.)
152. Hossenfelder, S., "Running coupling with minimal length", Phys. Rev. D, 70, 105003 (2004). [DOI], [arXiv:hep-ph/0405127 [hep-ph]. (Cited on page 61.)
153. Hossenfelder, S., "Suppressed black hole production from minimal length", Phys. Lett. B, 598, 92-98 (2004). [DOI], [arXiv:hep-th/0404232 [hep-th]. (Cited on page 61.)
154. Hossenfelder, S., "Interpretation of quantum field theories with a minimal length scale", Phys. Rev. D, 73, 105013 (2006). [DOI], [arXiv:hep-th/0603032 [hep-th]. (Cited on page 47.)
155. Hossenfelder, S., "Self-consistency in theories with a minimal length", Class. Quantum Grav., 23, 1815-1821 (2006). [DOI], [arXiv:hep-th/0510245 [hep-th]. (Cited on pages 50 and 58.)
156. Hossenfelder, S., "Deformed Special Relativity in Position Space", Phys. Lett. B, 649, 310-316 (2007). [DOI], [arXiv:gr-qc/0612167 [gr-qc]. (Cited on pages 48 and 58.)
157. Hossenfelder, S., "Multi-Particle States in Deformed Special Relativity", Phys. Rev. D, 75, 105005 (2007). [DOI], [arXiv:hep-th/0702016 [hep-th]. (Cited on pages 56 and 61.)
158. Hossenfelder, S., "A note on quantum field theories with a minimal length scale", Class. Quantum Grav., 25, 038003 (2008). [DOI], [arXiv:0712.2811 [hep-th]. (Cited on page 50.)
159. Hossenfelder, S., "The Box-Problem in Deformed Special Relativity", arXiv, e-print, (2009). [arXiv:0912.0090 [gr-qc]. (Cited on page 58.)
160. Hossenfelder, S., "Bounds on an energy-dependent and observer-independent speed of light from violations of locality", Phys. Rev. Lett., 104, 140402 (2010). [DOI], [arXiv:1004.0418 [hep-ph]. (Cited on page 58.)
161. Hossenfelder, S., "Comment on arXiv:1007.0718 by Lee Smolin", arXiv, e-print, (2010). [arXiv:1008.1312 [gr-qc]. (Cited on page 58.)
162. Hossenfelder, S., "Comments on Nonlocality in Deformed Special Relativity, in reply to arXiv:1004.0664 by Lee Smolin and arXiv:1004.0575 by Jacob et al", arXiv, e-print, (2010). [arXiv:1005.0535 [gr-qc]. (Cited on page 58.)
163. Hossenfelder, S., "Reply to arXiv:1006.2126 by Giovanni Amelino-Camelia et al", arXiv, e-print, (2010). [arXiv:1006.4587 [gr-qc]. (Cited on page 58.)
164. Hossenfelder, S., "Experimental Search for Quantum Gravity", in Frignanni, V.R., ed., Classical and Quantum Gravity: Theory, Analysis and Applications, (Nova Science Publishers, Hauppauge, NY, 2011). [arXiv:1010.3420 [gr-qc]. (Cited on page 66.)
165. Hossenfelder, S., "Can we measure structures to a precision better than the Planck length?", Class. Quantum Grav., 29, 115011 (2012). [DOI], [arXiv:1205.3636 [gr-qc]. (Cited on page 22.)
166. Hossenfelder, S., "Comment on arXiv:1104.2019, 'Relative locality and the soccer ball problem,' by Amelino-Camelia et al", arXiv, e-print, (2012). [arXiv:1202.4066 [hep-th]. (Cited on page 56.)
167. Hossenfelder, S., Bleicher, M., Hofmann, S., Ruppert, J., Scherer, S. et al., "Collider signatures in the Planck regime", Phys. Lett. B, 575, 85-99 (2003). [DOI], [arXiv:hep-th/0305262 [hep-th]. (Cited on pages 59, 60, and 61.)
168. Hsu, S.D.H., "Quantum production of black holes", Phys. Lett. B, 555, 92-98 (2003). [DOI], [arXiv:hep-ph/0203154]. (Cited on page 13.)
169. Jacob, U., Mercati, F., Amelino-Camelia, G. and Piran, T., "Modifications to Lorentz invariant dispersion in relatively boosted frames", Phys. Rev. D, 82, 084021 (2010). [DOI], [arXiv:1004.0575 [astro-ph.HE]. (Cited on pages 48, 57, 58, and 62.)
170. Johnson, C.V., "D-Brane Primer", in Harvey, J., Kachru, S. and Silverstein, E., eds., Strings, Branes and Gravity (TASI 99), Boulder, Colorado, USA, 31 May-25 June 1999, pp. 129-350, (World Scientific, Singapore; River Edge, NJ, 2000). [DOI], [arXiv:hep-th/0007170 [hep-th], [Google Books]. (Cited on page 27.)
171. Judes, S. and Visser, M., "Conservation laws in 'Doubly special relativity'", Phys. Rev. D, 68, 045001 (2003). [DOI], [arXiv:gr-qc/0205067 [gr-qc]. (Cited on pages 56 and 62.)
172. Kalyana Rama, S., "Some consequences of the generalized uncertainty principle: Statistical mechanical, cosmological, and varying speed of light", Phys. Lett. B, 519, 103-110 (2001). [DOI], [arXiv:hep-th/0107255 [hep-th]. (Cited on page 62.)
173. Karliner, M., Klebanov, I.R. and Susskind, L., "Size and shape of strings", Int. J. Mod. Phys. A, 3, 1981 (1988). [DOI]. (Cited on page 25.)
174. Kempf, A., "Quantum groups and quantum field theory with nonzero minimal uncertainties in positions and momenta", Czech. J. Phys., 44, 1041-1048 (1994). [DOI], [arXiv:hep-th/9405067]. (Cited on pages 9 and 60.)
175. Kempf, A., "Uncertainty relation in quantum mechanics with quantum group symmetry", J. Math. Phys., 35, 4483-4496 (1994). [DOI], [arXiv:hep-th/9311147]. (Cited on pages 9, 48, and 50.)
176. Kempf, A., "On Noncommutative Geometric Regularisation", Phys. Rev. D, 54, 5174-5178 (1996). [DOI], [arXiv:hep-th/9602119]. (Cited on page 60.)
177. Kempf, A., "Non-pointlike particles in harmonic oscillators", J. Phys. A: Math. Gen., 30, 2093-2102 (1997). [DOI], [arXiv:hep-th/9604045 [hep-th]. (Cited on page 59.)
178. Kempf, A., "On quantum field theory with nonzero minimal uncertainties in positions and momenta", J. Math. Phys., 38, 1347-1372 (1997). [DOI], [arXiv:hep-th/9602085]. (Cited on pages 9 and 60.)
179. Kempf, A., "Fields over unsharp coordinates", Phys. Rev. Lett., 85, 2873 (2000). [DOI], [arXiv:hepth/ 9905114 [hep-th]. (Cited on page 65.)
180. Kempf, A., "Mode generating mechanism in inflation with cutoff", Phys. Rev. D, 63, 083514 (2001). [DOI], [arXiv:astro-ph/0009209]. (Cited on page 9.)
181. Kempf, A., "Covariant Information-Density Cutoff in Curved Space-Time", Phys. Rev. Lett., 92, 221301 (2004). [DOI], [arXiv:gr-qc/0310035]. (Cited on page 65.)
182. Kempf, A., "Spacetime could be simultaneously continuous and discrete in the same way that information can", New J. Phys., 12, 115001 (2010). [DOI], [arXiv:1010.4354 [gr-qc]. (Cited on page 65.)
183. Kempf, A. and Mangano, G., "Minimal length uncertainty relation and ultraviolet regularization", Phys. Rev. D, 55, 7909-7920 (1997). [DOI], [arXiv:hep-th/9612084 [hep-th]. (Cited on page 60.)
184. Kempf, A., Mangano, G. and Mann, R.B., "Hilbert space representation of the minimal length uncertainty relation", Phys. Rev. D, 52, 1108-1118 (1995). [DOI], [arXiv:hep-th/9412167]. (Cited on pages 9, 50, and 59.)
185. Kim, W., Kim, Y.-W. and Park, Y.-J., "Entropy of the Randall-Sundrum brane world with the generalized uncertainty principle", Phys. Rev. D, 74, 104001 (2006). [DOI], [arXiv:gr-qc/0605084 [gr-qc]. (Cited on page 64.)
186. Kim, W., Son, E.J. and Yoon, M., "Thermodynamics of a black hole based on a generalized uncertainty principle", J. High Energy Phys., 2008(01), 035 (2008). [DOI], [arXiv:0711.0786 [gr-qc]. (Cited on page 64.)
187. Kiritsis, E., Introduction to Superstring Theory, Leuven Notes in Mathematical and Theoretical Physics, (Leuven University Press, Leuven, 1998). [arXiv:hep-th/9709062]. (Cited on page 22.)
188. Kober, M., "Gauge Theories under Incorporation of a Generalized Uncertainty Principle", Phys. Rev. D, 82, 085017 (2010). [DOI], [arXiv:1008.0154 [physics.gen-ph]. (Cited on pages 60 and 61.)
189. Kober, M., "Electroweak Theory with a Minimal Length", Int. J. Mod. Phys. A, 26, 4251-4285 (2011). [DOI], [arXiv:1104.2319 [hep-ph]. (Cited on page 61.)
190. Kober, M., "Generalized Quantization Principle in Canonical Quantum Gravity and Application to Quantum Cosmology", Int. J. Mod. Phys. A, 27, 1250106 (2012). [DOI], [arXiv:1109.4629 [gr-qc]. (Cited on page 61.)
191. Kostelecky, V. Alan and Russell, N., "Data Tables for Lorentz and CPT Violation", Rev. Mod. Phys., 83, 11 (2011). [DOI], [arXiv:0801.0287 [hep-ph]. (Cited on page 62.)
192. Kothawala, D., Sriramkumar, L., Shankaranarayanan, S. and Padmanabhan, T., "Path integral duality modified propagators in spacetimes with constant curvature", Phys. Rev. D, 80, 044005 (2009). [DOI], [arXiv:0904.3217 [hep-th]. (Cited on page 64.)
193. Kowalski-Glikman, J., "Observer independent quantum of mass", Phys. Lett. A, 286, 391-394 (2001). [DOI], [arXiv:hep-th/0102098 [hep-th]. (Cited on page 46.)
194. Kowalski-Glikman, J., "Doubly special quantum and statistical mechanics from quantum κ-Poincaré algebra", Phys. Lett. A, 299, 454-460 (2002). [DOI], [arXiv:hep-th/0111110 [hep-th]. (Cited on page 62.)
195. Kowalski-Glikman, J., "Introduction to Doubly Special Relativity", in Amelino-Camelia, G. and Kowalski-Glikman, J., eds., Planck Scale Effects in Astrophysics and Cosmology, 40th Karpacz Winter School of Theoretical Physics, Ladek Zdrój, Poland, 4-14 February 2004, Lecture Notes in Physics, 669, pp. 131-159, (Springer, Berlin; New York, 2005). [DOI], [arXiv:hep-th/0405273 [hepth]. (Cited on page 56.)
196. Kowalski-Glikman, J., "An introduction to relative locality", unpublished, (2013). (Cited on page 62.)
197. Kowalski-Glikman, J. and Nowak, S., "Doubly special relativity and de Sitter space", Class. Quantum Grav., 20, 4799-4816 (2003). [DOI], [arXiv:hep-th/0304101 [hep-th]. (Cited on pages 54, 55, and 56.)
198. Kowalski-Glikman, J. and Starodubtsev, A., "Effective particle kinematics from Quantum Gravity", Phys. Rev. D, 78, 084039 (2008). [DOI], [arXiv:0808.2613 [gr-qc]. (Cited on page 66.)
199. Kragh, H., "Arthur March, Werner Heisenberg, and the search for a smallest length", Rev. Hist. Sci., 48, 401-434 (1995). [DOI]. (Cited on page 8.)
200. Lévi, R., "Théorie de l'action universelle et discontinue", J. Phys. Radium, 8, 182-198 (1927). [DOI]. (Cited on page 6.)
201. Li, X., "Black hole entropy without brick walls", Phys. Lett. B, 540, 9-13 (2002). [DOI], [arXiv:grqc/ 0204029 [gr-qc]. (Cited on page 64.)
202. Litim, D.F., "Fixed Points of Quantum Gravity and the Renormalisation Group", in From Quantum to Emergent Gravity: Theory and Phenomenology, June 11-15 2007, Trieste, Italy, Proceedings of Science, PoS(QG-Ph)024, (SISSA, Trieste, 2008). [arXiv:0810.3675 [hep-th]. URL (accessed 15 November 2012): http://pos.sissa.it/cgi-bin/reader/conf.cgi?confid=43. (Cited on page 38.)
203. Loll, R., "Discrete Approaches to Quantum Gravity in Four Dimensions", Living Rev. Relativity, 1, lrr-1998-13 (1998). [arXiv:gr-qc/9805049 [gr-qc]. URL (accessed 11 October 2011): http://www.livingreviews.org/lrr-1998-13. (Cited on page 44.)
204. Lowe, D.A., Polchinski, J., Susskind, L., Thorlacius, L. and Uglum, J., "Black hole complementarity versus locality", Phys. Rev. D, 52, 6997-7010 (1995). [DOI], [arXiv:hep-th/9506138]. (Cited on page 25.)
205. Lukierski, J., Nowicki, A. and Ruegg, H., "New quantum Poincaré algebra and κ-deformed field theory", Phys. Lett. B, 293, 344-352 (1992). [DOI]. (Cited on page 54.)
206. Lukierski, J., Ruegg, H. and Zakrzewski, W.J., "Classical and Quantum Mechanics of Free κ-Relativistic Systems", Ann. Phys. (N.Y.), 243, 90-116 (1995). [DOI], [arXiv:hep-th/9312153 [hepth]. (Cited on page 65.)
207. Maggiore, M., "The Algebraic structure of the generalized uncertainty principle", Phys. Lett. B, 319, 83-86 (1993). [DOI], [arXiv:hep-th/9309034 [hep-th]. (Cited on page 48.)
208. Maggiore, M., "A generalized uncertainty principle in quantum gravity", Phys. Lett. B, 304, 65-69 (1993). [DOI], [arXiv:hep-th/9301067]. (Cited on page 18.)
209. Maggiore, M., "Quantum groups, gravity and the generalized uncertainty principle", Phys. Rev. D, 49, 5182-5187 (1994). [DOI], [arXiv:hep-th/9305163 [hep-th]. (Cited on page 48.)
210. Magueijo, J., "Could quantum gravity be tested with high intensity lasers?", Phys. Rev. D, 73, 124020 (2006). [DOI], [arXiv:gr-qc/0603073 [gr-qc]. (Cited on page 56.)
211. Magueijo, J. and Smolin, L., "Lorentz invariance with an invariant energy scale", Phys. Rev. Lett., 88, 190403 (2002). [DOI], [arXiv:hep-th/0112090 [hep-th]. (Cited on page 61.)
212. Magueijo, J. and Smolin, L., "Generalized Lorentz invariance with an invariant energy scale", Phys. Rev. D, 67, 044017 (2003). [DOI], [arXiv:gr-qc/0207085 [gr-qc]. (Cited on pages 46 and 56.)
213. Majid, S. and Ruegg, H., "Bicrossproduct structure of κ-Poincare group and non-commutative geometry", Phys. Lett. B, 334, 348-354 (1994). [DOI], [arXiv:hep-th/9405107]. (Cited on pages 9, 54, and 55.)
214. Majumder, B., "Black Hole Entropy and the Modified Uncertainty Principle: A heuristic analysis", Phys. Lett. B, 703, 402-405 (2011). [DOI], [arXiv:1106.0715 [gr-qc]. (Cited on page 64.)
215. Majumder, B., "Effects of GUP in Quantum Cosmological Perfect Fluid Models", Phys. Lett. B, 699, 315-319 (2011). [DOI], [arXiv:1104.3488 [gr-qc]. (Cited on page 64.)
216. Majumder, B., "The Generalized Uncertainty Principle and the Friedmann equations", Astrophys. Space Sci., 336, 331-335 (2011). [DOI], [arXiv:1105.2425 [gr-qc]. (Cited on page 64.)
217. Majumder, B., "Quantum Black Hole and the Modified Uncertainty Principle", Phys. Lett. B, 701, 384-387 (2011). [DOI], [arXiv:1105.5314 [gr-qc]. (Cited on page 64.)
218. Manrique, E., Rechenberger, S. and Saueressig, F., "Asymptotically Safe Lorentzian Gravity", Phys. Rev. Lett., 106, 251302 (2011). [DOI], [arXiv:1102.5012 [hep-th]. (Cited on page 68.)
219. March, A., "Die Geometrie kleinster Räume", Z. Phys., 104, 93 (1936). (Cited on pages 6 and 64.)
220. Martin, J. and Brandenberger, R.H., "The trans-Planckian problem of inflationary cosmology", Phys. Rev. D, 63, 123501 (2001). [DOI], [arXiv:hep-th/0005209]. (Cited on pages 9 and 67.)
221. Maziashvili, M., "Implications of minimum-length deformed quantum mechanics for QFT/QG", Fortschr. Phys., (2013). [DOI], [arXiv:1110.0649 [gr-qc]. (Cited on page 61.)
222. Mead, C.A., "Possible Connection Between Gravitation and Fundamental Length", Phys. Rev., 135, B849-B862 (1964). [DOI]. (Cited on pages 9, 11, 14, 15, 17, and 68.)
223. Mead, C.A., "Observable Consequences of Fundamental-Length Hypotheses", Phys. Rev., 143, 990-1005 (1966). [DOI]. (Cited on page 9.)
224. Mead, C.A. and Wilczek, F., "Walking the Planck Length through History", Phys. Today, 54, 15 (2001). [DOI]. (Cited on page 9.)
225. Medved, A.J.M. and Vagenas, E.C., "When conceptual worlds collide: The GUP and the BH entropy", Phys. Rev. D, 70, 124021 (2004). [DOI], [arXiv:hep-th/0411022 [hep-th]. (Cited on page 64.)
226. Meljanac, S. and Samsarov, A., "Scalar field theory on κ-Minkowski space-time and translation and Lorentz invariance", Int. J. Mod. Phys. A, 26, 1439-1468 (2011). [DOI], [arXiv:1007.3943 [hep-th]. (Cited on page 60.)
227. Mena Marugán, G.A., Olmedo, J. and Pawlowski, T., "Prescriptions in Loop Quantum Cosmology: A comparative analysis", Phys. Rev. D, 84, 064012 (2011). [DOI], [arXiv:1108.0829 [gr-qc]. (Cited on page 34.)
228. Mende, P.F. and Ooguri, H., "Borel summation of string theory for Planck scale scattering", Nucl. Phys. B, 339, 641-662 (1990). [DOI]. (Cited on page 24.)
229. Mercuri, S., "Introduction to Loop Quantum Gravity", in Pinheiro, C., de Arruda, A.S., Blas, H. and Pires, G.O., eds., 5th International School on Field Theory and Gravitation, April 20-24, 2009, Cuiabá, Brazil, Proceedings of Science, PoS(ISFTG)016, (SISSA, Trieste, 2009). [arXiv:1001.1330 [gr-qc]. URL (accessed 15 November 2012): http://pos.sissa.it/cgi-bin/reader/conf.cgi?confid=81. (Cited on page 32.)
230. Mignemi, S., "Doubly special relativity and translation invariance", Phys. Lett. B, 672, 186-189 (2009). [DOI], [arXiv:0808.1628 [gr-qc]. (Cited on page 53.)
231. Mimasu, K. and Moretti, S., "Top quark phenomenology of the Arkani-Hamed-Dimopoulos-Dvali model and the minimal length scenario", Phys. Rev. D, 85, 074019 (2012). [DOI], [arXiv:1108.3280 [hep-ph]. (Cited on page 61.)
232. Moayedi, S.K., Setare, M.R. and Moayeri, H., "Quantum Gravitational Corrections to the Real Klein-Gordon Field in the Presence of a Minimal Length", Int. J. Theor. Phys., 49, 2080-2088 (2010). [DOI], [arXiv:1004.0563 [hep-th]. (Cited on page 60.)
233. Moayedi, S.K., Setare, M.R. and Moayeri, H., "Formulation of the Spinor Field in the Presence of a Minimal Length Based on the Quesne-Tkachuk Algebra", Int. J. Mod. Phys. A, 26, 4981-4990 (2011). [DOI], [arXiv:1105.1900 [hep-th]. (Cited on page 60.)
234. Möglich, F., "Über das Massenverhältnis Elektron-Neutron", Die Naturwissenschaften, 26, 409-410 (1938). [DOI]. (Cited on page 6.)
235. Mohaupt, T., "Introduction to string theory", in Giulini, D., Kiefer, C. and Lämmerzahl, C., eds., Quantum Gravity: From Theory to Experimental Search, 271th WE-Heraeus Seminar 'Aspects of Quantum Gravity', Bad Honnef, Germany, 24 February-1 March 2002, Lecture Notes in Physics, 631, pp. 173-251, (Springer, Berlin; New York, 2003). [DOI], [arXiv:hep-th/0207249]. (Cited on page 22.)
236. Moyal, J.E., "Quantum mechanics as a statistical theory", Proc. Cambridge Philos. Soc., 45, 99-124 (1949). [DOI]. (Cited on page 42.)
237. Myung, Y.S., Kim, Y.-W. and Park, Y.-J., "Black hole thermodynamics with generalized uncertainty principle", Phys. Lett. B, 645, 393-397 (2007). [DOI], [arXiv:gr-qc/0609031 [gr-qc]. (Cited on page 64.)
238. Ng, Y.J. and van Dam, H., "Limitation to quantum measurements of space-time distances", Ann. N.Y. Acad. Sci., 755, 579-584 (1995). [DOI], [arXiv:hep-th/9406110]. (Cited on page 20.)
239. Nicolini, P., "Noncommutative Black Holes, The Final Appeal To Quantum Gravity: A Review", Int. J. Mod. Phys. A, 24, 1229-1308 (2009). [DOI], [arXiv:0807.1939 [hep-th]. (Cited on page 66.)
240. Niedermaier, M. and Reuter, M., "The Asymptotic Safety Scenario in Quantum Gravity", Living Rev. Relativity, 9, lrr-2006-5 (2006). URL (accessed 20 January 2012): http://www.livingreviews.org/lrr-2006-5. (Cited on page 38.)
241. Nouicer, K., "Casimir effect in the presence of minimal lengths", J. Phys. A: Math. Gen., 38, 10027-10035 (2005). [DOI], [arXiv:hep-th/0512027 [hep-th]. (Cited on page 59.)
242. Nozari, K. and Fazlpour, B., "Generalized uncertainty principle, modified dispersion relations and early universe thermodynamics", Gen. Relativ. Gravit., 38, 1661-1679 (2006). [DOI], [arXiv:grqc/ 0601092 [gr-qc]. (Cited on page 62.)
243. Nozari, K. and Mehdipour, S.H., "Gravitational uncertainty and black hole remnants", Mod. Phys. Lett. A, 20, 2937-2948 (2005). [DOI], [arXiv:0809.3144 [gr-qc]. (Cited on page 64.)
244. Nozari, K. and Pedram, P., "Minimal length and bouncing-particle spectrum", Europhys. Lett., 92, 50013 (2010). [DOI], [arXiv:1011.5673 [hep-th]. (Cited on page 59.)
245. Nozari, K., Pedram, P. and Molkara, M., "Minimal Length, Maximal Momentum and the Entropic Force Law", Int. J. Theor. Phys., 51, 1268-1275 (2012). [DOI], [arXiv:1111.2204 [gr-qc]. (Cited on page 64.)
246. Olmo, G.J., "Palatini Actions and Quantum Gravity Phenomenology", J. Cosmol. Astropart. Phys., 2011(10), 018 (2011). [DOI], [arXiv:1101.2841 [gr-qc]. (Cited on page 56.)
247. Padmanabhan, T., "Physical Significance of Planck Length", Ann. Phys. (N.Y.), 165, 38-58 (1985). [DOI]. (Cited on pages 36 and 63.)
248. Padmanabhan, T., "Planck length as the lower bound to all physical length scales", Gen. Relativ. Gravit., 17, 215-221 (1985). [DOI]. (Cited on page 36.)
249. Padmanabhan, T., "Limitations on the operational definition of space-time events and quantum gravity", Class. Quantum Grav., 4, L107-L113 (1987). [DOI]. (Cited on page 63.)
250. Padmanabhan, T., "Duality and zero point length of space-time", Phys. Rev. Lett., 78, 1854-1857 (1997). [DOI], [arXiv:hep-th/9608182 [hep-th]. (Cited on page 63.)
251. Padmanabhan, T., "Hypothesis of path integral duality. I. Quantum gravitational corrections to the propagator", Phys. Rev. D, 57, 6206-6215 (1998). [DOI]. (Cited on page 63.)
252. Panella, O., "Casimir-Polder intermolecular forces in minimal length theories", Phys. Rev. D, 76, 045012 (2007). [DOI], [arXiv:0707.0405 [hep-th]. (Cited on page 59.)
253. Panes, B., "Minimum length-maximum velocity", Eur. Phys. J. C, 72, 1930 (2012). [DOI], [arXiv:1112.3753 [hep-ph]. (Cited on page 49.)
254. Pauli, W., "[899] Pauli an Heisenberg, 11. Juli 1947", in von Meyenn, K., ed., Wolfgang Pauli. Wissenschaftlicher Briefwechsel mit Bohr, Einstein, Heisenberg u. a, Bd. III: 1940-1949, Sources in the History of Mathematics and Physical Sciences, 11, pp. 461-464, (Springer, Berlin; New York, 1993). Online version (accessed 12 January 2012): http://cdsweb.cern.ch/record/84589. (Cited on page 8.)
255. Pedram, P., "A higher order GUP with minimal length uncertainty and maximal momentum", Phys. Lett. B, 714, 317-323 (2011). [DOI], [arXiv:1110.2999 [hep-th]. (Cited on page 59.)
256. Pedram, P., "Minimal Length and the Quantum Bouncer: A Nonperturbative Study", Int. J. Theor. Phys., 51, 1901-1910 (2012). [DOI], [arXiv:1201.2802 [hep-th]. (Cited on page 59.)
257. Pedram, P., "New Approach to Nonperturbative Quantum Mechanics with Minimal Length Uncertainty", Phys. Rev. D, 85, 024016 (2012). [DOI], [arXiv:1112.2327 [hep-th]. (Cited on pages 59 and 62.)
258. Pedram, P., "A note on the one-dimensional hydrogen atom with minimal length uncertainty", arXiv, e-print, (2012). [arXiv:1203.5478 [quant-ph]. (Cited on page 59.)
259. Pedram, P., Nozari, K. and Taheri, S.H., "The effects of minimal length and maximal momentum on the transition rate of ultra cold neutrons in gravitational field", J. High Energy Phys., 2011(03), 093 (2011). [DOI], [arXiv:1103.1015 [hep-th]. (Cited on page 59.)
260. Percacci, R., "Asymptotic Safety", in Oriti, D., ed., Approaches to Quantum Gravity: Towards a New Understanding of Space, Time and Matter, pp. 111-128, (Cambridge University Press, Cambridge; New York, 2009). [arXiv:0709.3851 [hep-th]. (Cited on page 38.)
261. Percacci, R. and Vacca, G.P., "Asymptotic Safety, Emergence and Minimal Length", Class. Quantum Grav., 27, 245026 (2010). [DOI], [arXiv:1008.3621 [hep-th]. (Cited on pages 38, 39, 40, and 57.)
262. Peres, A. and Rosen, N., "Quantum Limitations on the Measurement of Gravitational Fields", Phys. Rev., 118, 335-336 (1960). [DOI]. (Cited on page 8.)
263. Pérez-Payán, S., Sabido, M. and Yee, C., "Effects of deformed phase space on scalar field cosmology", arXiv, e-print, (2011). [arXiv:1111.6136 [hep-th]. (Cited on page 65.)
264. Pikovski, I., Vanner, M.R., Aspelmeyer, M., Kim, M.S. and Brukner, Č., "Probing Planck-scale physics with quantum optics", Nature Phys., 8, 393-397 (2012). [DOI], [ADS], [arXiv:1111.1979 [quant-ph]. (Cited on pages 62 and 67.)
265. Planck, M., " Über irreversible Strahlungsvorgänge", Ann. Phys. (Berlin), 1, 69 (1900). [DOI]. (Cited on page 6.)
266. Pokrowski, G.I., "Zur Frage nach der Struktur der Zeit", Z. Phys., 51, 737-739 (1928). [DOI]. (Cited on page 6.)
267. Proca, A. and Goudsmit, S., "Sur la masse des particules élémentaires", J. Phys. Radium, 10, 209-214 (1939). [DOI]. (Cited on page 6.)
268. Quesne, C. and Tkachuk, V.M., "Composite system in deformed space with minimal length", Phys. Rev. A, 81, 012106 (2010). [DOI], [arXiv:0906.0050 [hep-th]. (Cited on page 62.)
269. Raghavan, R.S., "Time-Energy Uncertainty in Neutrino Resonance: Quest for the Limit of Validity of Quantum Mechanics", arXiv, e-print, (2009). [arXiv:0907.0878 [hep-ph]. (Cited on page 65.)
270. Reuter, M. and Schwindt, J.-M., "A minimal length from the cutoff modes in asymptotically safe quantum gravity", J. High Energy Phys., 2006(01), 070 (2006). [DOI], [arXiv:hep-th/0511021 [hepth]. (Cited on page 39.)
271. Rovelli, C. and Smolin, L., "Discreteness of area and volume in quantum gravity", Nucl. Phys. B, 442, 593-622 (1995). [DOI], [arXiv:gr-qc/9411005]. (Cited on page 34.)
272. Rychkov, V.S., "Observers and measurements in noncommutative space-times", J. Cosmol. Astropart. Phys., 2003(07), 006 (2003). [DOI], [arXiv:hep-th/0305187 [hep-th]. (Cited on page 57.)
273. Said, J.L. and Adami, K.Z., "The generalized uncertainty principle in f(R) gravity for a charged black hole", Phys. Rev. D, 83, 043008 (2011). [DOI], [arXiv:1102.3553 [gr-qc]. (Cited on page 64.)
274. Salecker, H. and Wigner, E.P., "Quantum limitations of the measurement of space-time distances", Phys. Rev., 109, 571-577 (1958). [DOI]. (Cited on page 16.)
275. Scardigli, F., "Generalized uncertainty principle in quantum gravity from micro-black hole gedanken experiment", Phys. Lett., B452, 39-44 (1999). [DOI], [arXiv:hep-th/9904025]. (Cited on page 13.)
276. Scardigli, F. and Casadio, R., "Generalized uncertainty principle, extra dimensions and holography", Class. Quantum Grav., 20, 3915-3926 (2003). [DOI], [arXiv:hep-th/0307174 [hep-th]. (Cited on page 64.)
277. Schutzhold, R. and Unruh, W.G., "Large-scale nonlocality in 'doubly special relativity' with an energy-dependent speed of light", JETP Lett., 78, 431-435 (2003). [DOI], [arXiv:gr-qc/0308049 [grqc]. (Cited on page 58.)
278. Schwarz, J.H., "Introduction to superstring theory", arXiv, e-print, (2000). [arXiv:hep-ex/0008017]. (Cited on page 22.)
279. Sefiedgar, A.S., Nozari, K. and Sepangi, H.R., "Modified dispersion relations in extra dimensions", Phys. Lett. B, 696, 119-123 (2011). [DOI], [arXiv:1012.1406 [gr-qc]. (Cited on page 64.)
280. Setare, M.R., "Corrections to the Cardy-Verlinde formula from the generalized uncertainty principle", Phys. Rev. D, 70, 087501 (2004). [DOI], [arXiv:hep-th/0410044 [hep-th]. (Cited on page 64.)
281. 5 black holes", Int. J. Mod. Phys. A, 21, 1325-1332 (2006). [DOI], [arXiv:hep-th/0504179 [hep-th]. (Cited on page 64.)
282. Shankaranarayanan, S. and Padmanabhan, T., "Hypothesis of path integral duality: Applications to QED", Int. J. Mod. Phys. D, 10, 351-366 (2001). [DOI], [arXiv:gr-qc/0003058 [gr-qc]. (Cited on page 64.)
283. Shenker, S.H., "Another Length Scale in String Theory?", arXiv, e-print, (1995). [arXiv:hepth/ 9509132]. (Cited on page 27.)
284. Sindoni, L., "Emergent Models for Gravity: an Overview of Microscopic Models", SIGMA, 8, 027 (2012). [DOI], [arXiv:1110.0686 [gr-qc]. URL (accessed 20 November 2012): http://sigma-journal.com/2012/027/. (Cited on page 44.)
285. Smailagic, A., Spallucci, E. and Padmanabhan, T., "String theory T-duality and the zero point length of spacetime", arXiv, e-print, (2003). [arXiv:hep-th/0308122]. (Cited on pages 31 and 32.)
286. Smolin, L., "On limitations of the extent of inertial frames in non-commutative relativistic spacetimes", arXiv, e-print, (2010). [arXiv:1007.0718 [gr-qc]. (Cited on pages 48, 57, 58, and 62.)
287. Smolin, L., "Classical paradoxes of locality and their possible quantum resolutions in deformed special relativity", Gen. Relativ. Gravit., 43, 3671-3691 (2011). [DOI], [arXiv:1004.0664 [gr-qc]. (Cited on pages 48, 54, 57, 58, and 62.)
288. Snyder, H.S., "Quantized Space-Time", Phys. Rev., 71, 38-41 (1947). [DOI]. (Cited on pages 8 and 52.)
289. Snyder, H.S., "[817] Snyder an Pauli, 1946", in von Meyenn, K., ed., Wissenschaftlicher Briefwechsel mit Bohr, Einstein, Heisenberg u.a., Bd. III: 1940-1949, Sources in the History of Mathematics and Physical Sciences, 11, pp. 358-360, (Springer, Berlin; New York, 1993). (Cited on page 8.)
290. Sorkin, R.D., "Causal sets: Discrete gravity", in Gomberoff, A. and Marolf, D., eds., Lectures on Quantum Gravity, Pan-American Advanced Studies Institute School on Quantum Gravity, held at the CECS, Valdivia, Chile, January 4-14, 2002, Series of the Centro de Estudios Científicos, pp. 305-327, (Springer, New York, 2005). [arXiv:gr-qc/0309009 [gr-qc]. (Cited on page 44.)
291. Spallucci, E. and Fontanini, M., "Zero-point Length, Extra-Dimensions and String T-duality", in Grece, S.A., ed., New Developments in String Theory Research, pp. 245-270, (Nova Science Publishers, Hauppauge, NY, 2005). [arXiv:gr-qc/0508076]. (Cited on page 31.)
292. Sprenger, M., Nicolini, P. and Bleicher, M., "Neutrino oscillations as a novel probe for a minimal length", Class. Quantum Grav., 28, 235019 (2011). [DOI], [arXiv:1011.5225 [hep-ph]. (Cited on page 59.)
293. Sprenger, M., Nicolini, P. and Bleicher, M., "Physics on the smallest scales: an introduction to minimal length phenomenology", Eur. J. Phys., 33, 853-862 (2012). [DOI], [arXiv:1202.1500 [physics.edph]. (Cited on page 66.)
294. Srinivasan, K., Sriramkumar, L. and Padmanabhan, T., "Hypothesis of path integral duality. II. Corrections to quantum field theoretic results", Phys. Rev. D, 58, 044009 (1998). [DOI], [arXiv:grqc/ 9710104 [gr-qc]. (Cited on page 64.)
295. Sriramkumar, L. and Shankaranarayanan, S., "Path integral duality and Planck scale corrections to the primordial spectrum in exponential inflation", J. High Energy Phys., 2006(12), 050 (2006). [DOI], [arXiv:hep-th/0608224 [hep-th]. (Cited on page 64.)
296. Stetsko, M.M., "Harmonic oscillator with minimal length uncertainty relations and ladder operators", Phys. Rev. A, 74, 062105 (2006). [DOI], [arXiv:quant-ph/0703269 [quant-ph]. (Cited on page 59.)
297. Susskind, L., "String theory and the principles of black hole complementarity", Phys. Rev. Lett., 71, 2367-2368 (1993). [DOI], [arXiv:hep-th/9307168]. (Cited on page 23.)
298. Susskind, L., "Strings, black holes and Lorentz contraction", Phys. Rev. D, 49, 6606-6611 (1994). [DOI], [arXiv:hep-th/9308139]. (Cited on page 23.)
299. Szabo, R.J., "BUSSTEPP lectures on string theory: An introduction to string theory and D-brane dynamics", arXiv, e-print, (2002). [arXiv:hep-th/0207142]. (Cited on page 22.)
300. 't Hooft, G. and Veltman, M., "One-loop divergencies in the theory of gravitation", Ann. Inst. Henri Poincare A, 20, 69-94 (1974). Online version (accessed 20 November 2012): http://www.numdam.org/item?id=AIHPA_1974__20_1_69_0. (Cited on page 37.)
301. Tamaki, T., Harada, T., Miyamoto, U. and Torii, T., "Have we already detected astrophysical symptoms of space-time noncommutativity?", Phys. Rev. D, 65, 083003 (2002). [DOI], [arXiv:grqc/ 0111056 [gr-qc]. (Cited on pages 58 and 62.)
302. Tezuka, K.-I., "Uncertainty of Velocity in kappa-Minkowski Spacetime", arXiv, e-print, (2003). [arXiv:hep-th/0302126 [hep-th]. (Cited on page 57.)
303. Thiemann, T., "Closed formula for the matrix elements of the volume operator in canonical quantum gravity", J. Math. Phys., 39, 3347-3371 (1998). [DOI], [arXiv:gr-qc/9606091]. (Cited on page 34.)
304. Thiemann, T., "Loop quantum gravity: An inside view", in Stamatescu, I.-O. and Seiler, E., eds., Approaches to Fundamental Physics: An Assessment of Current Theoretical Ideas, Lecture Notes in Physics, 721, pp. 185-263, (Springer, Berlin; New York, 2007). [DOI], [arXiv:hep-th/0608210]. (Cited on page 32.)
305. Thiemann, T., Modern Canonical Quantum General Relativity, Cambridge Monographs on Mathematical Physics, (Cambridge University Press, Cambridge; New York, 2007). [arXiv:gr-qc/0110034]. (Cited on page 32.)
306. Thorne, K.S., "Nonspherical gravitational collapse: A short review", in Klauder, J.R., ed., Magic Without Magic: John Archibald Wheeler. A Collection of Essays in Honor of his Sixtieth Birthday, pp. 231-258, (W.H. Freeman, San Francisco, 1972). (Cited on page 13.)
307. Tomassini, L. and Viaggiu, S., "Physically motivated uncertainty relations at the Planck length for an emergent non-commutative spacetime", Class. Quantum Grav., 28, 075001 (2011). [DOI], [arXiv:1102.0894 [gr-qc]. (Cited on page 21.)
308. Unruh, W.G., "Sonic analog of black holes and the effects of high frequencies on black hole evaporation", Phys. Rev. D, 51, 2827-2838 (1995). [DOI]. (Cited on page 9.)
309. Vakili, B., "Cosmology with minimal length uncertainty relations", Int. J. Mod. Phys. D, 18, 1059-1071 (2009). [DOI], [arXiv:0811.3481 [gr-qc]. (Cited on page 64.)
310. Veneziano, G., "An enlarged uncertainty principle from gedanken string collisions?", in Arnowitt, R.L., Bryan, R. and Duff, M.J., eds., Strings '89, 3rd International Superstring Workshop, Texas A&M University, College Station, TX, March 13-8, 1989, pp. 86-103, (World Scientific, Singapore, 1990). Online version (accessed 29 March 2012): http://cdsweb.cern.ch/record/197729/. (Cited on pages 10 and 24.)
311. Vilela Mendes, R., "Some consequences of a non-commutative space-time structure", Eur. Phys. J. C, 42, 445-452 (2005). [DOI], [arXiv:hep-th/0406013 [hep-th]. (Cited on page 61.)
312. Wang, P., Yang, H. and Zhang, X., "Quantum gravity effects on compact star cores", arXiv, e-print, (2011). [arXiv:1110.5550 [gr-qc]. (Cited on page 63.)
313. Wess, J., "Nonabelian gauge theories on noncommutative spaces", in Nath, P., Zerwas, P.M. and Grosche, C., eds., The 10th International Conference On Supersymmetry And Unification Of Fundamental Interactions (SUSY02), June 17-23, 2002, DESY Hamburg, pp. 586-599, (DESY, Hamburg, 2002). Online version (accessed 29 March 2012): http://www-library.desy.de/preparch/desy/proc/proc02-02.html. (Cited on page 8.)
314. Wohlgenannt, M., "Non-commutative Geometry & Physics", Ukr. J. Phys., 55, 5-14 (2010). [arXiv:hep-th/0602105 [hep-th]. URL (accessed 15 November 2012): http://ujp.bitp.kiev.ua/index.php?item=j&id=122. (Cited on page 42.)
315. Xiang, L. and Wen, X.Q., "Black hole thermodynamics with generalized uncertainty principle", J. High Energy Phys., 2009(10), 046 (2009). [DOI], [arXiv:0901.0603 [gr-qc]. (Cited on page 64.)
316. Yang, C.N., "On quantized space-time", Phys. Rev., 72, 874 (1947). [DOI]. (Cited on page 8.)
317. Yoneya, T., "On the interpretation of minimal length in string theories", Mod. Phys. Lett. A, 4, 1587 (1989). [DOI]. (Cited on page 26.)
318. Yoneya, T., "String theory and space-time uncertainty principle", Prog. Theor. Phys., 103, 1081-1125 (2000). [DOI], [arXiv:hep-th/0004074]. (Cited on pages 24, 25, 26, 27, 28, and 29.)
319. Yoon, M., Ha, J. and Kim, W., "Entropy of Reissner-Nordstrom black holes with minimal length revisited", Phys. Rev. D, 76, 047501 (2007). [DOI], [arXiv:0706.0364 [gr-qc]. (Cited on page 64.)
320. Zhang, X., Shao, L. and Ma, B.-Q., "Photon Gas Thermodynamics in Doubly Special Relativity", Astropart. Phys., 34, 840-845 (2011). [DOI], [arXiv:1102.2613 [hep-th]. (Cited on page 63.)
321. Zhao, H.-X., Li, H.-F., Hu, S.-Q. and Zhao, R., "Generalized Uncertainty Principle and Black Hole Entropy of Higher-Dimensional de Sitter Spacetime", Commun. Theor. Phys., 48, 465-468 (2007). [DOI], [arXiv:gr-qc/0608023 [gr-qc]. (Cited on page 64.)