Bargmann invariants and geometric phases: A generalized connection

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 60, Issue 5, 1999, Pages 3397-3409

  Rabei, Eqab M ^a   Mukunda, N ^b   Simon, R ^c  

^a MUTAH UNIVERSITY   (Jordan)

^b INDIAN INSTITUTE OF SCIENCE   (India)

^c INSTITUTE OF MATHEMATICAL SCIENCES   (India)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000053287     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.60.3397     Document Type: Article

References (29)

1. M. V. Berry, Proc. R. Soc. London, Ser. A 392, 45 (1984).
2. Many of the early papers on geometric phase have been reprinted in Geometric Phases in Physics, edited by A. Shapere and F. Wilczek (World Scientific, Singapore, 1989), and in
3. Fundamentals of Quantum Optics, edited by G. S. Agarwal, SPIE Milestone Series (SPIE, Bellington, 1995).
4. Y. Aharonov and J. Anandan, Phys. Rev. Lett. 58, 1593 (1987).
5. J. Samuel and R. Bhandari, Phys. Rev. Lett. 60, 2339 (1988).
6. F. Wilczek and A. Zee, Phys. Rev. Lett. 52, 2111 (1984).
7. N. Mukunda and R. Simon, Ann. Phys. (N.Y.) 228, 205 (1993)
8. Ann. Phys. (N.Y.)N. MukundaR. Simon228, 269 (1993).
9. W. R. Hamilton (unpublished);L. C. Biedenharn and J. D. Louck, Angular Momentum in Quantum Physics. Encyclopedia of Mathematics and its applications (Addison-Wesley, Reading, MA, 1981), Vol. 8.
10. Hamilton’s theory of turns has been generalized to the simplest noncompact semisimple group (Formula presented) in R. Simon, N. Mukunda, and E. C. G. Sudarshan, Phys. Rev. Lett. 62, 1331 (1989)
11. R. SimonN. MukundaE. C. G. SudarshanJ. Math. Phys. 30, 1000 (1989);S. Chaturvedi, V. Srinivasan, R. Simon, and N. Mukunda (unpublished).
12. R. Simon and N. Mukunda, J. Phys. A: Math. Gen. 25, 6135 (1992).
13. V. Bargmann, J. Math. Phys. 5, 862 (1964).
14. E. P. Wigner, Group Theory (Academic, NY, 1959)
15. J. Samuel, Pramana, J. Phys. 48, 959 (1997).
16. D. Page, Phys. Rev. A 36, 3479 (1987).
17. S. Kobayashi and K. Nomizu, Foundations of Differential Geometry (Interscience, NY, 1969), Vol. II, Chap. IX.
18. S. Pancharatnam, Proc.-Indian Acad. Sci., Sect. A 44, 247 (1956); See also
19. S. Ramaseshan and R. Nityananda, Curr. Sci. 55, 1225 (1986)
20. M. V. Berry, J. Mod. Opt. 34, 1401 (1987).
21. G. Khanna, S. Mukhopadhyay, R. Simon, and N. Mukunda, Ann. Phys. (N.Y.) 253, 55 (1997)
22. Arvind, K. S. Mallesh, and N. Mukunda, J. Phys. A: Math. Gen. 30, 2417 (1997).
23. S. Chaturvedi, M. S. Sriram, and V. Srinivasan, J. Phys. A 20, L1071 (1987).
24. M. Berger, Geometry II (Springer-Verlag, Berlin, 1987), Chap. 19;
25. G. A. Jones and D. Singerman, Complex Functions: An Algebraic and Geometric Viewpoint (Cambridge University Press, Cambridge, 1987), Chap. 5.
26. R. Simon and N. Mukunda, Phys. Rev. Lett. 70, 880 (1993).
27. G. Gouy, C. R. Hebd. Seances Acad. Sci. 110, 125 (1890)
28. A. E. Siegman, Lasers (Oxford University Press, Oxford, 1986), Chap. 17.
29. B. Simon, Phys. Rev. Lett. 51, 2167 (1983).