A geometric renormalization group in discrete quantum space-time

Journal of Mathematical Physics

Volumn 44, Issue 12, 2003, Pages 5588-5615

  Requardt, Manfred ^a  

^a UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0344287504     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1619579     Document Type: Conference Paper

References (56)

1. F. Markopoulou and L. Smolin, Nucl. Phys. B 508, 409 (1997); gr-qc/9702025.
2. F. Markopoulou, "Dual Evolution of Spin Networks," gr-qc/9704013.
3. F. Markopoulou, "An Algebraic Approach to Coarse Graining," hep-th/0006199.
4. S. Kauffman and L. Smolin, "Combinatorial Dynamics in Quantum Gravity," "To wards Quantum Gravity," Proc. Polanica, edited by J. Kowalski-Glikman, Springer Lecture Notes in Physics (Springer, New York, 2000).
5. J. Baez, Class. Quantum Grav. 15, 1827 (1998); gr-qc/9709052.
6. J. Baez, "Spin Foam Models of BF Theory and Quantum Gravity," Lecture Notes in Physics (Springer, New York, 2000), p. 543, gr-qc/9905087.
7. L. Crane, "Hypergravity and Categorical Feynmanology," gr-qc/0004043.
8. J. W. Barrett and L. Crane, "A Lorentzian Signature Model for Quantum General Relativity," gr-qc/9904025.
9. L. Bombelli, J. Lee, D. Meyer, and R. Sorkin, Phys. Rev. Lett. 59, 521 (1987).
10. R. Sorkin, "A Specimen of Theory Construction from Quantum Gravity," in The Creation of Ideas in Physics, edited by J. Leplin (Kluwer, Dordrecht, 1995); gr-qc/9511063.
11. R. Sorkin, Int. J. Theor. Phys. 30, 923 (1991).
12. G. Brightwell and R. Gregory, Phys. Rev. Lett 66, 260 (1991).
13. D. P. Rideaut and R. Sorkin, Phys. Rev. D 61, 024002 (2000); gr-qc/9904062.
14. D. P. Rideaut and R. Sorkin, "Evidence for a Continuum Limit in Causal Set Dynamics," gr-qc/0003117.
15. T. Filk, Class. Quantum Grav. 18, 2785 (2001); gr-qc/0102088.
16. F. Antonsen, Int. J. Theor. Phys. 33, 1189 (1994).
17. C. J. Isham, "An Introduction to General Topology and Quantum Topology," Summer Inst. on Physics, Geometry and Topology, Banff, August 1989, Imperial/TP/88-89/30.
18. C. J. Isham, "Some Reflections on the Structure of Conventional Quantum Theory when applied to Quantum Gravity," quant-ph/0206090.
19. I. Raptis and R. Zapatrin, Class. Quantum Grav. 20, 4187 (2001); gr-qc/0102048.
20. G.'t Hooft, J. Stat. Phys. 53, 323 (1988).
21. G.'t Hooft, Nucl. Phys. B 342, 471 (1990).
22. G.'t Hooft, "Quantum Gravity and Dissipative Deterministic Systems," gr-qc/9903084.
23. T. Nowotny and M. Requardt, J. Phys. A 31, 2447 (1998); hep-th/9707082.
24. T. Nowotny and M. Requardt, J. Chaos, Solitons Fractals 10, 469 (1999); hep-th/9801199.
25. M. Requardt, J. Phys. A 31, 7997 (1998); hep-th/9806135.
26. M. Requardt, Class. Quantum Grav. 17, 2029 (2000): gr-qc/9912059.
27. M. Requardt, J. Phys. A 35, 759 (2002); math-ph/0001026.
28. M. Requardt and S. Roy, Class. Quantum Grav. 18, 3039 (2001); gr-qc/0011076.
29. M. Requardt, "The Translocal Depth-Structure of Space-Time," hep-th/0205168.
30. C. W. Misner, K. S. Thorne, J. A. Wheeler, Gravitation (Freeman, San Francisco, 1973).
31. C. W. Misner and J. A. Wheeler, Ann. Phys. (N.Y.) 2, 525 (1957).
32. J. A. Wheeler, Ann. Phys. (N.Y.) 2, 604 (1957).
33. J. Myrheim, "Statistical Geometry," Cern-Preprint Th.2538, 1978.
34. H. S. Snyder, Phys. Rev. 71, 38 (1947).
35. S. Doplicher, K. Fredenhagen, and J. E. Roberts, Commun. Math. Phys. 172, 187 (1995).
36. J. Madore and J. Mourad, J. Math. Phys. 39, 423 (1998).
37. T. D. Lee, in Selected Papers, Vol. 3, Random Lattices to Gravity, edited by G. Feinberg (Birkhaeuser, Boston, 1986).
38. J. Ambjorn, M. Carfora, and A. Marzuoli, "The Geometry of Dynamical Triangulation," in Lect. Notes Phys. Vol. 50, (Springer, New York, 1997); hep-th/9612069.
39. J. Ambjorn, B. Durhuus, and T. Jonsson, Quantum Geometry (Cambridge University Press, Cambridge, 1997).
40. A. Dachinski, Cellular Automata, A Discrete Universe (World Scientific, Singapore 2001), Secs. 8.8 and 12.
41. A. Ilachinski and P. Halpern, Complex Syst. 1, 503 (1987).
42. R. Albert and A. L. Barabasi, Rev. Mod. Phys. 74, 47 (2002).
43. A. L. Barabasi and E. Bonabeau, Sci. Am. 288 (5), 50 (2003).
44. M. Berger, Not Am. Math. Soc. 47, 183 (2000); 47, 326 (2000).
45. M. Berger, Not Am. Math. Soc. 47, 183 (2000); 47, 326 (2000).
46. P. de la Harpe, Topics in Geometric Group Theory (Univ. Chicago, Chicago, 2000).
47. L. Bartholdi and T. G. Checherini-Sibeistein, "Growth Series and Random Walks on some Hyperbolic Groups," math.GR/0109069.
48. L. Bartholdi, R. Grigorchuk, and V. Nekrashevych, "From Fractal Groups to Fractal Sets," math.GR/0202001.
49. B. Bollobas, Random Graphs (Academic, New York, 1985).
50. J. W. Gibbs, Statistical Mechanics, German edition (A. Barth Verlag, Leipzig, 1905).
51. B. Bollobas, Combinatorics (Cambridge University Press, London, 1986).
52. T. Nowotny, Diploma Thesis, Goettingen 1998, a compilation of some of the extensive computer simulations can be found on his web site: http://inls.ucsd.edu/novotny/
53. G. Birkhoff, Lattice Theory (AMS, Providence, 1961), Vol. XXV.
54. M. Aigner, Combinatorial Theory (Springer, New York, 1979).
55. J. Stillwell, Classical Topology and Combinatorial Group Theory (Springer, New York, 1993).
56. P. Bak, How Nature Works, the science of self-organized criticality (Springer, New York, 1996).