Polymer quantization, singularity resolution, and the 1/r2 potential

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 79, Issue 3, 2009, Pages

  Kunstatter, Gabor ^a   Louko, Jorma ^b   Ziprick, Jonathan ^c  

^a UNIVERSITY OF WINNIPEG   (Canada)

^b UNIVERSITY OF NOTTINGHAM   (United Kingdom)

^c UNIVERSITY OF MANITOBA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; QUANTUM THEORY;

ANTI-SYMMETRIC; BOUND STATE; COUPLING CONSTANTS; EIGENENERGIES; HIGHLY EXCITED STATE; LOW-LYING STATE; POLYMER THEORIES; POSITIVE REALS; QUANTIZATION SCHEMES; SEMICLASSICAL LIMITS;

POLYMERS;

EID: 63049098121     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.79.032104     Document Type: Article

References (48)

1. T. Thiemann, Modern Canonical Quantum General Relativity (Cambridge University Press, Cambridge, 2007).
2. A. Ashtekar, T. Pawlowski, and P. Singh, Phys. Rev. D 74, 084003 (2006); 10.1103/PhysRevD.74.084003
3. A. Ashtekar, T. Pawlowski, P. Singh, and K. Vandersloot, Phys. Rev. D 75, 024035 (2007); 10.1103/PhysRevD.75.024035
4. K. Vandersloot, Phys. Rev. D 75, 023523 (2007); 10.1103/PhysRevD.75. 023523
5. M. V. Battisti, O. M. Lecian, and G. Montani, Phys. Rev. D 78, 103514 (2008). 10.1103/PhysRevD.78.103514
6. M. Martin-Benito, L. J. Garay, and G. A. Mena Marugan, Phys. Rev. D 78, 083516 (2008). 10.1103/PhysRevD.78.083516
7. V. Husain and O. Winkler, Phys. Rev. D 73, 124007 (2006). 10.1103/PhysRevD.73.124007
8. A. Ashtekar and M. Bojowald, Class. Quantum Grav. 23, 391 (2006). 10.1088/0264-9381/23/2/008
9. L. Modesto, Class. Quantum Grav. 23, 5587 (2006); 10.1088/0264-9381/23/ 18/006
10. L. Modesto, eprint arXiv:gr-qc/0611043;
11. C. G. Bohmer and K. Vandersloot, Phys. Rev. D 76, 104030 (2007); 10.1103/PhysRevD.76.104030
12. C. G. Bohmer and K. Vandersloot, Phys. Rev. D 78, 067501 (2008); 10.1103/PhysRevD.78.067501
13. M. Campiglia, R. Gambini, and J. Pullin, Loop Quantization of Spherically Symmetric Midisuperspaces: The Interior Problem, AIP Conf. Proc. No. 977 (AIP, New York, 2008) p. 520;
14. R. Gambini and J. Pullin, Phys. Rev. Lett. 101, 161301 (2008). 10.1103/PhysRevLett.101.161301
15. T. Thiemann, Class. Quantum Grav. 15, 839 (1998). 10.1088/0264-9381/15/4/ 011
16. A. Ashtekar, S. Fairhurst, and J. L. Willis, Class. Quantum Grav. 20, 1031 (2003). 10.1088/0264-9381/20/6/302
17. H. Halvorson, Stud. Hist. Philos. Mod. Phys. 35, 45 (2004). 10.1016/j.shpsb.2003.01.001
18. C. J. Fewster, e-print arXiv:hep-th/9305102.
19. J. Louko and J. Mäkelä, Phys. Rev. D 54, 4982 (1996). 10.1103/PhysRevD.54.4982
20. V. Husain, J. Louko, and O. Winkler, Phys. Rev. D 76, 084002 (2007). 10.1103/PhysRevD.76.084002
21. L. Motl, Adv. Theor. Math. Phys. 6, 1135 (2003).
22. G. Kunstatter, Phys. Rev. Lett. 90, 161301 (2003). 10.1103/PhysRevLett. 90.161301
23. H. E. Camblong and C. R. Ordonez, Phys. Rev. D 71, 104029 (2005). 10.1103/PhysRevD.71.104029
24. J. Gegenberg, G. Kunstatter, and R. D. Small, Class. Quantum Grav. 23, 6087 (2006). 10.1088/0264-9381/23/22/001
25. K. M. Case, Phys. Rev. 80, 797 (1950). 10.1103/PhysRev.80.797
26. W. M. Frank, D. J. Land, and R. M. Spector, Rev. Mod. Phys. 43, 36 (1971). 10.1103/RevModPhys.43.36
27. H. Narnhofer, Acta Phys. Austriaca 40, 306 (1974).
28. K. S. Gupta and S. G. Rajeev, Phys. Rev. D 48, 5940 (1993). 10.1103/PhysRevD.48.5940
29. H. E. Camblong, L. N. Epele, H. Fanchiotti, and C. A. Garcia Canal, Phys. Rev. Lett. 85, 1590 (2000); 10.1103/PhysRevLett.85.1590
30. H. E. Camblong, L. N. Epele, H. Fanchiotti, and C. A. Garcia Canal, Ann. Phys. (N.Y.) 287, 14 (2001). 10.1006/aphy.2000.6092
31. H. E. Camblong and C. R. Ordonez, Phys. Lett. A 345, 22 (2005); 10.1016/j.physleta.2005.06.110
32. H. E. Camblong and C. R. Ordonez, Phys. Rev. D 68, 125013 (2003); 10.1103/PhysRevD.68.125013
33. G. N. J. Ananos, H. E. Camblong, and C. R. Ordonez, Phys. Rev. D 68, 025006 (2003). 10.1103/PhysRevD.68.025006
34. H. E. Camblong, L. N. Epele, H. Fanchiotti, C. A. Garcia Canal, and C. R. Ordonez, Phys. Lett. A 364, 458 (2007). 10.1016/j.physleta.2006.12.041
35. T. Fúlöp, in Proceedings of the Third Microconference "Analytic and Algebraic Methods III", Prague, 2007, edited by, M. Znojil
36. [Symmetry, Integr. Geom.: Methods Appl. 3, 107, (2007)];
37. http://www.emis.de/journals/SIGMA/Prague2007.html
38. W. E. Thirring, Quantum Mathematical Physics, 2nd ed. (Springer, Berlin, 2002).
39. Handbook of Mathematical Functions, edited by, M. Abramowitz, and, I. A. Stegun, (Dover, New York, 1965).
40. A. Corichi, T. Vukasinac, and J. A. Zapata, Phys. Rev. D 76, 044016 (2007). 10.1103/PhysRevD.76.044016
41. N. Andersson and C. J. Howls, Class. Quantum Grav. 21, 1623 (2004). 10.1088/0264-9381/21/6/021
42. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 4th ed. (Academic, New York, 1980).
43. M. Reed and B. Simon, Methods of Modern Mathematical Physics II: Fourier Analysis, Self-adjointness (Academic, New York, 1975).
44. S. Elaydi, An Introduction to Difference Equations, 3rd ed. (Springer, New York, 2005).
45. A. Ashtekar, A. Corichi, and P. Singh, Phys. Rev. D 77, 024046 (2008). 10.1103/PhysRevD.77.024046
46. A. Corichi and P. Singh, Phys. Rev. D 78, 024034 (2008). 10.1103/PhysRevD.78.024034
47. W. Kaminski and J. Lewandowski, Class. Quantum Grav. 25, 035001 (2008). 10.1088/0264-9381/25/3/035001
48. G. Kunstatter, J. Louko and J. Ziprick (unpublished).