The inverse loop transform

Journal of Mathematical Physics

Volumn 39, Issue 2, 1998, Pages 1236-1248

  Thiemann, T ^a  

^a ALBERT EINSTEIN INSTITUT   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032340790     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532344     Document Type: Article

References (46)

1. R. Gambini and A. Trias, Phys. Rev. D 22, 1380 (1980); C. Di Bartolo, F. Nori, R. Gambini, and A. Trias, Lett. Nuovo Cimento 38, 497 (1983).
2. R. Gambini and A. Trias, Phys. Rev. D 22, 1380 (1980); C. Di Bartolo, F. Nori, R. Gambini, and A. Trias, Lett. Nuovo Cimento 38, 497 (1983).
3. R. Giles, Phys. Rev. D 8, 2160 (1981).
4. C. Rovelli and L. Smolin, Nucl. Phys. B 331, 80 (1990).
5. A. Ashtekar, Phys. Rev. Lett. 57, 2244 (1986): Phys. Rev. D 36, 1587 (1987).
6. A. Ashtekar, Phys. Rev. Lett. 57, 2244 (1986): Phys. Rev. D 36, 1587 (1987).
7. A. Ashtekar and C. J. Isham. Class. Quantum Grav. 9, 1433 (1992).
8. A. Ashtekar and J. Lewandowski, "Representation theory of analytic holonomy C* algebras," in Knots and Quantum Gravity, edited by J. Baez (Oxford University Press, Oxford, 1994); J. Lewandowski, Int. J. Mod. Phys. D 3, 207 (1994).
9. A. Ashtekar and J. Lewandowski, "Representation theory of analytic holonomy C* algebras," in Knots and Quantum Gravity, edited by J. Baez (Oxford University Press, Oxford, 1994); J. Lewandowski, Int. J. Mod. Phys. D 3, 207 (1994).
10. J. Baez, Lett. Math. Phys. 31, 213 (1994); "Diffeomorphism invariant generalized measures on the space of connections modulo gauge transformations," hep-th/9305045, in Proceedings of the Conference on Quantum Topology, edited by D. Yetter (World Scientific, Singapore, 1994).
11. J. Baez, Lett. Math. Phys. 31, 213 (1994); "Diffeomorphism invariant generalized measures on the space of connections modulo gauge transformations," hep-th/9305045, in Proceedings of the Conference on Quantum Topology, edited by D. Yetter (World Scientific, Singapore, 1994).
12. D. Marolf and J. M. Mourão, Commun. Math. Phys. 170, 583 (1995); A. Ashtekar, D. Marolf, and J. Mourão, "Integration on the space of connections modulo gauge transformations" in The Proceedings of the Lanczos International Centenary Conference, edited by J. D. Brown et al. (SIAM, Philadelphia, 1994).
13. D. Marolf and J. M. Mourão, Commun. Math. Phys. 170, 583 (1995); A. Ashtekar, D. Marolf, and J. Mourão, "Integration on the space of connections modulo gauge transformations" in The Proceedings of the Lanczos International Centenary Conference, edited by J. D. Brown et al. (SIAM, Philadelphia, 1994).
14. J. Lewandowski, "Differential geometry for the space of connections modulo gauge transformations", in The Proceedings of the Lanczos International Centenary Conference, edited by J. D. Brown et al. (SIAM, Philadelphia, 1994); A. Ashtekar and J. Lewandowski, J. Geom. Phys. 17, 191 (1995).
15. J. Lewandowski, "Differential geometry for the space of connections modulo gauge transformations", in The Proceedings of the Lanczos International Centenary Conference, edited by J. D. Brown et al. (SIAM, Philadelphia, 1994); A. Ashtekar and J. Lewandowski, J. Geom. Phys. 17, 191 (1995).
16. A. Ashtekar and J. Lewandowski, J. Math. Phys. 36, 2170 (1995).
17. A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourão, and T. Thiemann, J. Math. Phys. 36, 6456 (1995).
18. A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourão, and T. Thiemann, J. Funct. Anal. 135, 519 (1996).
19. T. Thiemann, Class. Quantum Grav. 13, 1383 (1996).
20. A. Ashtekar, Phys. Rev. D 53, R2865 (1996).
21. T. Thiemann, Phys. Lett. B 380, 1383 (1996); "Quantum Spin Dynamics (QSD)," Harvard University preprint HUTMP-96/B-359, gr-qc/9606089 (to appear in Class. Quantum Grav.).
22. T. Thiemann, Phys. Lett. B 380, 1383 (1996); "Quantum Spin Dynamics (QSD)," Harvard University preprint HUTMP-96/B-359, gr-qc/9606089 (to appear in Class. Quantum Grav.).
23. F. Barbero, Phys. Rev. D 51, 5507 (1995).
24. T. Thiemann, Acta Cosmol. 21, 145 (1995).
25. J. Glimm and A. Jaffe, Quantum Physics (Springer-Verlag, New York, 1987); Y. Yamasaki, Measures on Infinite Dimensional Spaces (World Scientific, Singapore, 1985).
26. J. Glimm and A. Jaffe, Quantum Physics (Springer-Verlag, New York, 1987); Y. Yamasaki, Measures on Infinite Dimensional Spaces (World Scientific, Singapore, 1985).
27. A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourão, and T. Thiemann, "A manifestly gauge invariant approach to quantum theories of gauge fields," in Geometry of Constrained Dynamical Systems, edited by J. Charap (Cambridge University Press, Cambridge, 1994).
28. T. Thiemann, Banach Center Publications, 1996, Vol. 39, p. 389.
29. A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourão, and T. Thiemann, "SU(N) Yang-Mills Theory in two dimensions: A complete solution," J. Math. Phys. (in press).
30. O. Foster, Analysis 3 (Vieweg, Braunschweig/Wiesbaden, 1987).
31. C. Rovelli and L. Smolin, Phys. Rev. D 53, 5743 (1995).
32. J. Baez, Adv. Math. 117, 253 (1996); "Spin networks in non-perturbative quantum gravity," in The Interface of Knots and Physics, edited by L. Kauffman (American Mathematical Society, Providence, RI, 1996).
33. J. Baez, Adv. Math. 117, 253 (1996); "Spin networks in non-perturbative quantum gravity," in The Interface of Knots and Physics, edited by L. Kauffman (American Mathematical Society, Providence, RI, 1996).
34. N. J. Vilenkin, Special Functions and the Theory of Group Representations (American Mathematical Society, Providence, RI, 1968).
35. B. C. Hall, J. Funct. Anal. 122, 103 (1994).
36. W. Rudin, Real and Complex Analysis (McGraw-Hill, New York, 1987).
37. H. Boerner, Representations of Groups (North-Holland, Amsterdam, 1970).
38. H. Kodama, Phys. Rev. D 42, 2548 (1990).
39. R. Gambini and J. Pullin, Phys. Rev. D 54, 5935 (1996); H. Fort, R. Gambini, and J. Pullin, "Lattice knot theory and quantum gravity in the loop representation," gr-qc/9608033; R. Gambini, J. Griego, and J. Pullin, "Chern-Simons states in spin-network quantum gravity," gr-qc/9703042.
40. R. Gambini and J. Pullin, Phys. Rev. D 54, 5935 (1996); H. Fort, R. Gambini, and J. Pullin, "Lattice knot theory and quantum gravity in the loop representation," gr-qc/9608033; R. Gambini, J. Griego, and J. Pullin, "Chern-Simons states in spin-network quantum gravity," gr-qc/9703042.
41. R. Gambini and J. Pullin, Phys. Rev. D 54, 5935 (1996); H. Fort, R. Gambini, and J. Pullin, "Lattice knot theory and quantum gravity in the loop representation," gr-qc/9608033; R. Gambini, J. Griego, and J. Pullin, "Chern-Simons states in spin-network quantum gravity," gr-qc/9703042.
42. R. De Pietri and C. Rovelli, "Geometry eigenvalues and scalar product from recoupling theory in loop quantum gravity," Phys. Rev. D 54, 2664 (1996).
43. C. Rovelli and L. Smolin, Nucl. Phys. B 442, 593 (1995); 456, 5743 (1995); A. Ashtekar and J. Lewandowski, Class. Quantum Grav. 14, A55 (1997); T. Thiemann, "A length operator for canonical quantum gravity," Harvard University preprint HUTMP-96/B-354, gr-qc/9606092.
44. C. Rovelli and L. Smolin, Nucl. Phys. B 442, 593 (1995); 456, 5743 (1995); A. Ashtekar and J. Lewandowski, Class. Quantum Grav. 14, A55 (1997); T. Thiemann, "A length operator for canonical quantum gravity," Harvard University preprint HUTMP-96/B-354, gr-qc/9606092.
45. C. Rovelli and L. Smolin, Nucl. Phys. B 442, 593 (1995); 456, 5743 (1995); A. Ashtekar and J. Lewandowski, Class. Quantum Grav. 14, A55 (1997); T. Thiemann, "A length operator for canonical quantum gravity," Harvard University preprint HUTMP-96/B-354, gr-qc/9606092.
46. C. Rovelli and L. Smolin, Nucl. Phys. B 442, 593 (1995); 456, 5743 (1995); A. Ashtekar and J. Lewandowski, Class. Quantum Grav. 14, A55 (1997); T. Thiemann, "A length operator for canonical quantum gravity," Harvard University preprint HUTMP-96/B-354, gr-qc/9606092.