Heisenberg algebra in the Bargmann-Fock space with natural cutoffs

Advances in High Energy Physics

Volumn 2014, Issue , 2014, Pages

  Roushan, Maryam ^a   Nozari, Kourosh ^b  

^a ISLAMIC AZAD UNIVERSITY   (Iran)

^b UNIVERSITY OF MAZANDARAN   (Iran)

Author keywords

[No Author keywords available]

Indexed keywords

FOCK SPACES; HEISENBERG ALGEBRAS; MINIMAL LENGTHS; UNCERTAINTY PRINCIPLES;

ALGEBRA;

EID: 84897594237     PISSN: 16877357     EISSN: 16877365     Source Type: Journal    
DOI: 10.1155/2014/353192     Document Type: Article

References (37)

1. Veneziano G., A stringy nature needs just two constants. Europhysics Letters 1986 2 3, article 199 10.1209/0295-5075/2/3/006
2. Amati D., Cialfaloni M., Veneziano G., Superstring collisions at planckian energies. Physics Letters B 1987 197 1-2 81 88 10.1016/0370-2693(87) 90346-7
3. Amati D., Cialfaloni M., Veneziano G., Can spacetime be probed below the string size? Physics Letters B 1989 216 1-2 41 47 10.1016/0370-2693(89)91366-X
4. Gross D. J., Mende P. F., The high-energy behavior of string scattering amplitudes. Physics Letters B 1987 197 1-2 129 134 10.1016/0370-2693(87)90355-8 MR913246
5. Konishi K., Paffuti G., Provero P., Minimum physical length and the generalized uncertainty principle in string theory. Physics Letters B 1990 234 3 276 284 10.1016/0370-2693(90)91927-4 MR1036685
6. Guida R., Konishi K., Provero P., On the short distance behavior of string theories. Modern Physics Letters A 1991 6 16 1487 1504 10.1142/S0217732391001603
7. Kato M., Particle theories with minimum observable length and open string theory. Physics Letters B 1990 245 1 43 47
8. Garay L. J., Quantum gravity and minimal length. International Journal of Modern Physics A 1995 10 2 145 166
9. Capozziello S., Lambiase G., Scarpetta G., Generalized uncertainty principle from quantum geometry. International Journal of Theoretical Physics 2000 39 1 15 22 10.1023/A:1003634814685 MR1755014 ZBL0981.83021
10. Maggiore M., A generalized uncertainty principle in quantum gravity. Physics Letters B 1993 304 1-2 65 69 10.1016/0370-2693(93)91401-8 MR1253719
11. Maggiore M., The algebraic structure of the generalized uncertainty principle. Physics Letters B 1993 319 1-3 83 86 10.1016/0370-2693(93)90785-G MR1253719
12. Maggiore M., Quantum groups, gravity, and the generalized uncertainty principle. Physical Review D 1994 49 10 5182 5187 10.1103/PhysRevD.49.5182 MR1280422
13. Hossenfelder S., Minimal length scale scenarios for quantum gravity. Living Reviews in Relativity 2013 16 10.12942/lrr-2013-2
14. Hossenfelder S., Can we measure structures to a precision better than the Planck length? Classical and Quantum Gravity 2012 29 11 115011 ZBL1246.83077
15. Scardigli F., Generalized uncertainty principle in quantum gravity from micro-black hole gedanken experiment. Physics Letters B 1999 452 1-2 39 44
16. Kempf A., Mangano G., Mann R. B., Hilbert space representation of the minimal length uncertainty relation. Physical Review D 1995 52 2 1108 1118 10.1103/PhysRevD.52.1108 MR1344174
17. Hinrichsen H., Kempf A., Maximal localization in the presence of minimal uncertainties in positions and in momenta. Journal of Mathematical Physics 1996 37 5 2121 2137 10.1063/1.531501 MR1385820 ZBL0883.46049
18. Kempf A., On quantum field theory with nonzero minimal uncertainties in positions and momenta. Journal of Mathematical Physics 1997 38 3 1347 1372 10.1063/1.531814 MR1435673 ZBL0872.58009
19. Bojowald M., Kempf A., Generalized uncertainty principles and localization of a particle in discrete space. Physical Review D 2012 86 8 15 085017 10.1103/PhysRevD.86.085017
20. Nozari K., Etemadi A., Minimal length, maximal momentum, and Hilbert space representation of quantum mechanics. Physical Review D 2012 85 10 12 104029 10.1103/PhysRevD.85.104029
21. Nozari K., Fazlpour B., Some consequences of spacetime fuzziness. Chaos, Solitons & Fractals 2007 34 2 224 234 10.1016/j.chaos.2006.03.066 MR2271099 ZBL1132.83306
22. Amelino-Camelia G., Relativity in spacetimes with short-distance structure governed by an observer-independent (Planckian) length scale. International Journal of Modern Physics D 2000 11 1 35 60 10.1142/ S0218271802001330 MR1883132
23. Amelino-Camelia G., Relativity: special treatment. Nature 2002 418 34 35 10.1038/418034a
24. Amelino-Camelia G., Doubly-special relativity: first results and key open problems. International Journal of Modern Physics D 2002 11 10 1643 1669 10.1142/S021827180200302X MR1969145 ZBL1070.83500
25. Kowalski-Glikman J., Introduction to doubly special relativity. Planck Scale Effects in Astrophysics and Cosmology 2005 669 Berlin, Germany Springer 131 159 Lecture Notes in Physics 10.1007/11377306-5
26. Amelino-Camelia G., Kowalski-Glikman J., Mandanici G., Procaccini A., Phenomenology of doubly special relativity. International Journal of Modern Physics A 2005 20 26 6007 6037 10.1142/S0217751X05028569 MR2182602
27. Imilkowska K., Kowalski-Glikman J., Doubly special relativity as a limit of gravity. Special Relativity 2006 702 Berlin, Germany Springer 279 298 Lecture Notes in Physics 10.1007/3-540-34523-X-10 ZBL1151.83007
28. Magueijo J., Smolin L., Lorentz invariance with an invariant energy scale. Physical Review Letters 2002 88 19 4 190403 10.1103/PhysRevLett.88.190403
29. Magueijo J., Smolin L., Generalized Lorentz invariance with an invariant energy scale. Physical Review D 2003 67 4 12 044017 10.1103/PhysRevD.67.044017 MR1976712
30. Magueijo J., Smolin L., String theories with deformed energy-momentum relations, and a possible nontachyonic bosonic string. Physical Review D 2005 71 2 6 026010 10.1103/PhysRevD.71.026010 MR2125684
31. Cortés J. L., Gamboa J., Quantum uncertainty in doubly special relativity. Physical Review D 2005 71 6 4 065015 10.1103/PhysRevD.71.065015 MR2138847
32. Ali A. F., Das S., Vagenas E. C., Discreteness of space from the generalized uncertainty principle. Physics Letters B 2009 678 5 497 499 10.1016/j.physletb.2009.06.061 MR2555723
33. Das S., Vagenas E. C., Ali A. F., Discreteness of space from GUP II: relativistic wave equations. Physics Letters B 2010 690 4 407 412 10.1016/j.physletb.2010.05.052
34. Pedram P., Nozari K., Taheri S. H., The effects of minimal length and maximal momentum on the transition rate of ultra cold neutrons in gravitational field. Journal of High Energy Physics 2011 2011 3, article 93 10.1007/JHEP03(2011)093
35. Mirza B., Zarei M., Minimal uncertainty in momentum: the effects of IR gravity on quantum mechanics. Physical Review D 2009 79 12 8 125007 10.1103/PhysRevD.79.125007
36. Koekoek R., Swarttouw R. F., The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue. 1994 94-05 Delft, Netherlands Faculty of Technical Mathematics and Informatics, Delft University of Technology
37. Nozari K., Soleymani Z., Natural cutoffs and Hilbert space representation of quantum mechanics. 1514 Proceedings of the Multiverse and Fundamental Cosmology (Multicosmofun '12) September 2012 Szczecin, Poland 93 96 AIP Conference Proceedings 10.1063/1.4791733