Generaized coherent states and the diagonal representation for operators

Journal of Mathematical Physics

Volumn 44, Issue 6, 2003, Pages 2479-2506

  Mukunda, N ^a,b   Arvind, ^c,f   Chaturvedi, S ^d   Simon, R ^e  

^a INDIAN INSTITUTE OF SCIENCE   (India)

^b JAWAHARLAL NEHRU CENTRE FOR ADVANCED SCIENTIFIC RESEARCH   (India)

^c GURU NANAK DEV UNIVERSITY   (India)

^d UNIVERSITY OF HYDERABAD   (India)

^e INSTITUTE OF MATHEMATICAL SCIENCES   (India)

^f CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038683678     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1559416     Document Type: Article

References (42)

1. E. P. Wigner, Phys. Rev. 40, 749 (1932).
2. M. Hillery, R. F. O'Connell, M. O. Scully, and E. P. Wigner, Phys. Rep. 106, 121 (1984); Y. S. Kim and M. E. Noz, Phase Space Pictures of Quantum Mechanics (World Scientific, Singapore, 1991).
3. M. Hillery, R. F. O'Connell, M. O. Scully, and E. P. Wigner, Phys. Rep. 106, 121 (1984); Y. S. Kim and M. E. Noz, Phase Space Pictures of Quantum Mechanics (World Scientific, Singapore, 1991).
4. H. Weyl, The Theory of Groups and Quantum Mechanics (Dover, New York, 1931), p. 274.
5. P. A. M. Dirac, Rev. Mod. Phys. 17, 195 (1945).
6. H. J. Groenewold, Physica (Utrecht) 12, 405 (1946); J. E. Moyal, Proc. Cambridge Philos. Soc. 45, 99 (1949).
7. H. J. Groenewold, Physica (Utrecht) 12, 405 (1946); J. E. Moyal, Proc. Cambridge Philos. Soc. 45, 99 (1949).
8. K. E. Cahill and R. J. Glauber, Phys. Rev. 177, 1857 (1969); 177, 1882 (1969); G. S. Agarwal and E. Wolf, Phys. Rev. D 2, 2161 (1970); 2, 2187 (1970); 2, 2206 (1970).
9. K. E. Cahill and R. J. Glauber, Phys. Rev. 177, 1857 (1969); 177, 1882 (1969); G. S. Agarwal and E. Wolf, Phys. Rev. D 2, 2161 (1970); 2, 2187 (1970); 2, 2206 (1970).
10. K. E. Cahill and R. J. Glauber, Phys. Rev. 177, 1857 (1969); 177, 1882 (1969); G. S. Agarwal and E. Wolf, Phys. Rev. D 2, 2161 (1970); 2, 2187 (1970); 2, 2206 (1970).
11. K. E. Cahill and R. J. Glauber, Phys. Rev. 177, 1857 (1969); 177, 1882 (1969); G. S. Agarwal and E. Wolf, Phys. Rev. D 2, 2161 (1970); 2, 2187 (1970); 2, 2206 (1970).
12. K. E. Cahill and R. J. Glauber, Phys. Rev. 177, 1857 (1969); 177, 1882 (1969); G. S. Agarwal and E. Wolf, Phys. Rev. D 2, 2161 (1970); 2, 2187 (1970); 2, 2206 (1970).
13. R. J. Glauber, Phys. Rev. 131, 2766 (1963); E. C. G. Sudarshan, Phys. Rev. Lett. 10, 277 (1963).
14. R. J. Glauber, Phys. Rev. 131, 2766 (1963); E. C. G. Sudarshan, Phys. Rev. Lett. 10, 277 (1963).
15. K. Husimi, Proc. Phys. Math. Soc. Jpn. 22, 264 (1940); J. Kano, J. Math. Phys. 6, 1913 (1965); C. L. Mehta and E. C. G. Sudarshan, Phys. Rev. 138, B274 (1965).
16. K. Husimi, Proc. Phys. Math. Soc. Jpn. 22, 264 (1940); J. Kano, J. Math. Phys. 6, 1913 (1965); C. L. Mehta and E. C. G. Sudarshan, Phys. Rev. 138, B274 (1965).
17. K. Husimi, Proc. Phys. Math. Soc. Jpn. 22, 264 (1940); J. Kano, J. Math. Phys. 6, 1913 (1965); C. L. Mehta and E. C. G. Sudarshan, Phys. Rev. 138, B274 (1965).
18. J. R. Klauder, J. Math. Phys. 4, 1058 (1963).
19. A. M. Perelomov, Commun. Math. Phys. 26, 222 (1972).
20. J. M. Radcliffe, J. Phys. A 4, 343 (1971); F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Phys. Rev. A6, 2211 (1972).
21. J. M. Radcliffe, J. Phys. A 4, 343 (1971); F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Phys. Rev. A 6, 2211 (1972).
22. G. S. Agarwal, Phys. Rev. A 24, 2889 (1981).
23. J. R. Klauder and E. C. G. Sudarshan, Fundamentals of Quantum Optics (W. A. Benjamin, New York, 1968); L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
24. J. R. Klauder and E. C. G. Sudarshan, Fundamentals of Quantum Optics (W. A. Benjamin, New York, 1968); L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
25. A. P. Balachandran et al., "A fuzzy lens space L(3) and its *-product," Syracuse University preprint.
26. J. R. Klauder and B. Skagerstam, Coherent States: Applications in Physics and Mathematical Physics (World Scientific, Singapore, 1985), pp. 23 and 34.
27. C. Brif and A. Mann, J. Phys. A 31, L9 (1998); Phys. Rev. A 59, 971 (1999). See also, J. M. Garcia-Bondia and J. C. Várilly, J. Phys. A 18, L879 (1988); J. C. Várilly and J. M. Garcia-Bondiá, Ann. Phys. (N.Y.) 190, 107 (1989): J. F. Cariñena, J. M. Garcia-Bondiá, and J. C. Várilly, J. Phys. A 23, 901 (1990).
28. C. Brif and A. Mann, J. Phys. A 31, L9 (1998); Phys. Rev. A 59, 971 (1999). See also, J. M. Garcia-Bondia and J. C. Várilly, J. Phys. A 18, L879 (1988); J. C. Várilly and J. M. Garcia-Bondiá, Ann. Phys. (N.Y.) 190, 107 (1989): J. F. Cariñena, J. M. Garcia-Bondiá, and J. C. Várilly, J. Phys. A 23, 901 (1990).
29. C. Brif and A. Mann, J. Phys. A 31, L9 (1998); Phys. Rev. A 59, 971 (1999). See also, J. M. Garcia-Bondia and J. C. Várilly, J. Phys. A 18, L879 (1988); J. C. Várilly and J. M. Garcia-Bondiá, Ann. Phys. (N.Y.) 190, 107 (1989): J. F. Cariñena, J. M. Garcia-Bondiá, and J. C. Várilly, J. Phys. A 23, 901 (1990).
30. C. Brif and A. Mann, J. Phys. A 31, L9 (1998); Phys. Rev. A 59, 971 (1999). See also, J. M. Garcia-Bondia and J. C. Várilly, J. Phys. A 18, L879 (1988); J. C. Várilly and J. M. Garcia-Bondiá, Ann. Phys. (N.Y.) 190, 107 (1989): J. F. Cariñena, J. M. Garcia-Bondiá, and J. C. Várilly, J. Phys. A 23, 901 (1990).
31. C. Brif and A. Mann, J. Phys. A 31, L9 (1998); Phys. Rev. A 59, 971 (1999). See also, J. M. Garcia-Bondia and J. C. Várilly, J. Phys. A 18, L879 (1988); J. C. Várilly and J. M. Garcia-Bondiá, Ann. Phys. (N.Y.) 190, 107 (1989): J. F. Cariñena, J. M. Garcia-Bondiá, and J. C. Várilly, J. Phys. A 23, 901 (1990).
32. G. W. Mackey, Group Representations in Hilbert Space (AMS, Providence, RI, 1963).
33. L. K. Pandit and N. Mukunda, J. Math. Phys. 6, 1547 (1965).
34. F. Haake and M. Wilkens, "Quasi probabilities based on squeezed states" in Photons and Quantum Fluctuations, Malvern Physics Series, edited by E. R. Pike and H. Walther (Adam Hilger, New York, 1988); J. Stat. Phys. 53, 345 (1988).
35. F. Haake and M. Wilkens, "Quasi probabilities based on squeezed states" in Photons and Quantum Fluctuations, Malvern Physics Series, edited by E. R. Pike and H. Walther (Adam Hilger, New York, 1988); J. Stat. Phys. 53, 345 (1988).
36. S. M. Roy and V. Singh, Phys. Rev. D 25, 3413 (1982); M. Ventata Satyanarayana, ibid. 32, 400 (1985); F. A. M. de Oliviera, M. S. Kim, P. L. Knight, and V. Buzek, Phys. Rev. A 41, 2645 (1990); P. Kral, J. Mod. Opt. 37, 889 (1990).
37. S. M. Roy and V. Singh, Phys. Rev. D 25, 3413 (1982); M. Ventata Satyanarayana, ibid. 32, 400 (1985); F. A. M. de Oliviera, M. S. Kim, P. L. Knight, and V. Buzek, Phys. Rev. A 41, 2645 (1990); P. Kral, J. Mod. Opt. 37, 889 (1990).
38. S. M. Roy and V. Singh, Phys. Rev. D 25, 3413 (1982); M. Ventata Satyanarayana, ibid. 32, 400 (1985); F. A. M. de Oliviera, M. S. Kim, P. L. Knight, and V. Buzek, Phys. Rev. A 41, 2645 (1990); P. Kral, J. Mod. Opt. 37, 889 (1990).
39. S. M. Roy and V. Singh, Phys. Rev. D 25, 3413 (1982); M. Ventata Satyanarayana, ibid. 32, 400 (1985); F. A. M. de Oliviera, M. S. Kim, P. L. Knight, and V. Buzek, Phys. Rev. A 41, 2645 (1990); P. Kral, J. Mod. Opt. 37, 889 (1990).
40. C. Goebel, Phys. Rev. Lett. 16, 1130 (1966); T. Cook and B. Sakira, J. Math. Phys. 8, 708 (1967).
41. C. Goebel, Phys. Rev. Lett. 16, 1130 (1966); T. Cook and B. Sakira, J. Math. Phys. 8, 708 (1967).
42. N. Mukunda, J. Math. Phys. 10, 97 (1969).