The semiclassical propagator for spin coherent states

Journal of Mathematical Physics

Volumn 41, Issue 12, 2000, Pages 8025-8049

  Stone, Michael ^a   Park, Kee Su ^a   Garg, Anupam ^b  

^a University of Illinois at Urbana Champaign   (United States)

^b NORTHWESTERN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034367834     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1320856     Document Type: Article

References (41)

1. J. R. Klauder, Phys. Rev. D 19, 2349 (1979).
2. H. Kuratsuji and T. Suzuki, J. Math. Phys. 21, 472 (1980).
3. A. Jevicki and N. Papanicolaou, Ann. Phys. (N.Y.) 120, 107 (1979).
4. H. B. Nielsen and D. Röhrlich, Nucl. Phys. B 299, 471 (1988).
5. J. R. Klauder, in Path Integrals, in Proceedings of the NATO Advanced Summer Institute, edited by G. J. Papadopoulos and J. T. Devreese (Plenum, New York, 1978).
6. Path Integrals and Coherent States of SU(2) and SU(1,1), edited by H. Kuratsuji, A. Inomata, and C. C. Gerry (World Scientific, Singapore, 1992).
7. N. M. J. Woodhouse, Geometric Quantization (Oxford University Press, Oxford, 1992).
8. J. H. Duistermat and G. J. Heckman, Invent. Math. 69, 259 (1982); 72, 153 (1983).
9. J. H. Duistermat and G. J. Heckman, Invent. Math. 69, 259 (1982); 72, 153 (1983).
10. M. Stone, Nucl. Phys. B 314, 577 (1989).
11. E. Keskivakkuri, A. J. Niemi, G. Semenoff, and O. Tirkkonen, Phys. Rev. D 44, 3899 (1991).
12. E. M. Chudnovsky and L. Gunther, Phys. Rev. Lett. 60, 661 (1988).
13. D. Loss, D. P. Vincenzo, and G. Grinstein, Phys. Rev. Lett. 69, 3232 (1992).
14. J. von Delft and C. L. Henley, Phys. Rev. Lett. 69, 3236 (1992).
15. A. Garg, Europhys. Lett. 22, 205 (1993).
16. W. Wernsdorfer and R. Sessoli, Science 284, 133 (1999).
17. H. Kuratsuji and Y. Mizobuchi, J. Math. Phys. 22, 757 (1981).
18. A. Garg and G-H. Kim, Phys. Rev. B 45, 921 (1992).
19. M. Enz and R. Schilling, J. Phys. C 19, L711 (1986); 19, 1765 (1986).
20. M. Enz and R. Schilling, J. Phys. C 19, L711 (1986); 19, 1765 (1986).
21. V. I. Belinicher, C. Providencia, and J. da Providencia, J. Phys. A 30, 5633 (1997).
22. J. Shibata and S. Takagi, Int. J. Mod. Phys. B 13, 107 (1999).
23. J. L. Hemmen and A. Süto, Europhys. Lett. 1, 481 (1986); Physica B & C 141, 37 (1986).
24. J. L. Hemmen and A. Süto, Europhys. Lett. 1, 481 (1986); Physica B & C 141, 37 (1986).
25. A. Garg, Phys. Rev. Lett. 83, 4385 (1999); cond-mat/0003114; cond-mat/0003156.
26. J. Villain and A. Fort, Europhys. J. B 17, 69 (2000).
27. H. G. Solari, J. Math. Phys. 28, 1097 (1987).
28. E. A. Kochetov, J. Math. Phys. 36, 4667 (1995).
29. A. Perelomov, Generalized Coherent States and their Applications (Springer-Verlag, Berlin, 1986).
30. See, for example, R. Bott, Ann. Math. 66, 203 (1957).
31. A. A. Kirillov, Elements of the Theory of Representations (Springer-Verlag, Berlin, 1976).
32. E. Lieb, Commun. Math. Phys. 31, 327 (1973).
33. A. P. Balachandran, G. Marmo, B. S. Skagerstam, and A. Stern, Gauge Symmetries and Fiber Bundles (Springer-Verlag, Berlin, 1983); A. P. Balachandran, G. Marmo, B. S. Skagerstam, and A. Stern, Classical Topology and Quantum States (Springer-Verlag, Berlin, 1991).
34. A. P. Balachandran, G. Marmo, B. S. Skagerstam, and A. Stern, Gauge Symmetries and Fiber Bundles (Springer-Verlag, Berlin, 1983); A. P. Balachandran, G. Marmo, B. S. Skagerstam, and A. Stern, Classical Topology and Quantum States (Springer-Verlag, Berlin, 1991).
35. See, for example, R. D. Richtmyer, Principles of Advanced Mathematical Physics (Springer-Verlag, Berlin, 1978), Sec. 7.2.
36. The "shooting method" we used is described in S. Kos and M. Stone, Phys. Rev. B 59, 9545 (1999) (cond-mat/9809182).
37. M. S. Marinov, Phys. Rep. 60, 1 (1980).
38. E. Ercolessi, G. Morandi, F. Napoli, and R. Pieri, J. Math. Phys. 37, 535 (1996).
39. F. Funahashi, T. Kashiwa, S. Sakoda, and K. Fujii, J. Math. Phys. 36, 3232 (1995).
40. See, e.g., L. S. Schulman, Techniques and Applications of Path Integration (Wiley, New York, 1981), Chap. 23.
41. V. R. Vieira and P. D. Sacramento, Nucl. Phys. B 448, 331 (1995).