Polymer geometry at Planck scale and quantum Einstein equations

International Journal of Modern Physics D

Volumn 5, Issue 6, 1996, Pages 629-648

  Ashtekar, Abhay ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030327837     PISSN: 02182718     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218271896000400     Document Type: Article

References (54)

1. P. Faria de Veiga, Ecole Polytechnique thesis (1990); C. de Calan, P. Faria de Veiga, J. Magnen and R. Sénéor, Phy. Rev. Lett. 66 (1991) 3233; A. S. Wightman, in: Mathematical Physics Towards XXIst Centrury, eds R. N. Sen and A. Gersten (Ben Gurion University Press, 1994).
2. P. Faria de Veiga, Ecole Polytechnique thesis (1990); C. de Calan, P. Faria de Veiga, J. Magnen and R. Sénéor, Phy. Rev. Lett. 66 (1991) 3233; A. S. Wightman, in: Mathematical Physics Towards XXIst Centrury, eds R. N. Sen and A. Gersten (Ben Gurion University Press, 1994).
3. P. Faria de Veiga, Ecole Polytechnique thesis (1990); C. de Calan, P. Faria de Veiga, J. Magnen and R. Sénéor, Phy. Rev. Lett. 66 (1991) 3233; A. S. Wightman, in: Mathematical Physics Towards XXIst Centrury, eds R. N. Sen and A. Gersten (Ben Gurion University Press, 1994).
4. D. Amati, M. Ciafolini and G. Veneziano, Nucl. Phys. B347 (1990) 550.
5. A. Ashtekar, C. Rovelli and L. Smolin, Phys. Rev. Lett. 69 (1992) 237;
6. A. Agishtein and A. Migdal, Mod. Phys. Lett. 7 (1992) 85.
7. J. Iwasaki and C. Rovelli, Int. J. Mod. Phys. D1 (1993) 533; Class. & Quantum Grav. 11 (1994) 1653.
8. J. Iwasaki and C. Rovelli, Int. J. Mod. Phys. D1 (1993) 533; Class. & Quantum Grav. 11 (1994) 1653.
9. T. Jacobson and L. Smolin, Nucl. Phys. B299 (1988) 295.
10. C. Rovelli and L. Smolin, Phys. Rev. Lett. 72 (1994) 446.
11. A. Ashtekar, Non-Perturbative Canonical Gravity (World Scientific, Singapore, 1991); in Gravitation and Quantization eds B. Julia and j. Zinn-Justin (Elsevier, Amsterdam 1995).
12. A. Ashtekar, Non-Perturbative Canonical Gravity (World Scientific, Singapore, 1991); in Gravitation and Quantization eds B. Julia and j. Zinn-Justin (Elsevier, Amsterdam 1995).
13. R. Rovelli, Class. & Quantum Grav. 8 (1991) 1613.
14. L. Smolin, in Quantum Gravity and Cosmology eds J. P. Mercader, H. Solà and E. Verdaguer (World Scientific, Singapore, 1992).
15. R. Gambini and J. Pullin Loops, Knots, Gauge Theories and Quantum Gravity (Cambridge University Press, Cambridge, 1995).
16. A. Ashtekar, Phys. Rev. Lett. 57 (1986) 2244; Phys. Rev.D36 (1987) 1587.
17. A. Ashtekar, Phys. Rev. Lett. 57 (1986) 2244; Phys. Rev.D36 (1987) 1587.
18. A. Ashtekar, in Mathematics and General Relativity (AMS, Providence, 1987).
19. A. Ashtekar and C. J. Isham, Class. & Quantum Grav. 9 (1992) 1433.
20. J. C. Baez and S. Sawin, Functional integration of spaces of connections, q-alg/9507023.
21. A. Rendall, Class. & Quantum Grav. 10 (1993) 605.
22. A. Ashtekar and J. Lewandowski, in Knots and Quantum Gravity, ed J. Baez (Oxford University Press, Oxford, 1994).
23. J. Baez, Lett. Math. Phys.31 (1994) 213; in The Proceedings of the Conference on Quantum Topology, ed D. N. Yetter (World Scientific, Singapore, in press).
24. J. Baez, Lett. Math. Phys.31 (1994) 213; in The Proceedings of the Conference on Quantum Topology, ed D. N. Yetter (World Scientific, Singapore, in press).
25. D. Marolf and J. Morão, Commun. Math. Phys. 170 (1995) 583.
26. A. Ashtekar and J. Lewandowski, J. Math. Phys. 36 (1995) 2170.
27. A. Ashtekar and J. Lewandowski, J. Geo. & Phys. (in press).
28. A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourão and T. Thiemann, Coherent state transform on the space of connections, J. Fund. Analysis (in press).
29. A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourão and T. Thiemann, J. Math. Phys. (in press).
30. J. C. Baez, Spin networks in gauge theory, Adv. Math. (in press); Spin networks in non-perturbative quantum gravity, gr-qc/9504036.
31. J. C. Baez, Spin networks in gauge theory, Adv. Math. (in press); Spin networks in non-perturbative quantum gravity, gr-qc/9504036.
32. L. Smolin (private communication).
33. C. Rovelli and L. Smolin, Spin networks and quantum gravity, preprint CGPG-95/4-1.
34. R. Penrose, in Quantum Theory and Beyond, ed T. Bastin, Cambridge University Press, Cambridge 1971).
35. A. Ashtekar and J. Lewandowski, Quantum geometry, (preprint).
36. C. Rovelli and L. Smolin Nucl. Phys.B442, 593 (1995).
37. R. Loll, The volume operator in discretized gravity, (pre-print).
38. C. Rovelli, Nucl. Phys.B405 (1993) 797; L. Smolin, Phys. Rev.D49 (1994) 4028.
39. C. Rovelli, Nucl. Phys.B405 (1993) 797; L. Smolin, Phys. Rev.D49 (1994) 4028.
40. A. Higuchi, Class. & Quantum Grav.8 (1991) 1983; 2023; N. P. Landsman J. Geo. & Phys.15 (1995) 285.
41. A. Higuchi, Class. & Quantum Grav.8 (1991) 1983; 2023; N. P. Landsman J. Geo. & Phys.15 (1995) 285.
42. A. Ashtekar and R. S. Tate, J. Math. Phys. 34 (1994) 6434.
43. B. Brügmann and J. Pullin, Nucl. Phys. B363 (1991) 221; B390 (1993) 399.
44. B. Brügmann and J. Pullin, Nucl. Phys. B363 (1991) 221; B390 (1993) 399.
45. B. Brügmann, R. Gambini and J. Pullin, Phys. Rev. Lett. 68 (1992) 431.
46. H. Nicolai and H. J. Matschull, J. Geo. and Phys. 11 (1993) 15; H. J. Matschull, pre-print gr/qc 9305025;
47. H. Nicolai and H. J. Matschull, J. Geo. and Phys. 11 (1993) 15; H. J. Matschull, pre-print gr/qc 9305025;
48. H. A. Morales-Técotl and C. Rovelli, Phys. Rev. Lett.72 (1994) 3642.
49. C. Rovelli and L. Smolin (private communication).
50. A. Ashtekar and J. Lewandowski (in preparation).
51. K. Kuchař (private communication).
52. T. Thiemann (in preparation).
53. A. Ashtekar (in preparation).
54. A. Ashtekar and L. Bombelli (in preparation).