The geometric phase and ray space isometrics

Pramana - Journal of Physics

Volumn 48, Issue 5, 1997, Pages 959-967

  Samuel, Joseph ^a  

^a RAMAN RESEARCH INSTITUTE   (India)

Author keywords

Geometric phase; Symmetry in quantum mechanics

Indexed keywords

MATHEMATICAL TRANSFORMATIONS; THEOREM PROVING;

GEOMETRIC PHASE; HILBERT SPACE; PANCHARATNAM PHASE; RAY SPACE ISOMETRIES;

QUANTUM THEORY;

EID: 0031144782     PISSN: 03044289     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02847455     Document Type: Article

References (21)

1. A symmetry of a quantum system is also required to leave the Hamiltonian invariant. This is not relevant here as we will not be concerned with Hamiltonians in this paper
2. E P Wigner, Group theory (Academic Press Inc., NY, 1959)
3. V Bargmann, J. Math. Phys. 5, 862 (1964)
4. G Emch and C Piron, J. Math. Phys. 4, 469 (1963)
5. A Shapere and F Wilczek, Geometric phases in physics (World Scientific, Singapore, 1989)
6. N Mukunda and R Simon, Ann. Phys. (NY) 228, 205 (1993)
7. M V Berry, Proc. R. Soc. A392, 45 (1984)
8. B Simon, Phys. Rev. Lett. 51, 2167 (1983)
9. Y Aharonov and J Anandan, Phys. Rev. Lett. 58, 1593 (1987)
10. S Ramaseshan and R Nityananda, Curr. Sci. (India) 55, 1225 (1986)
11. S Pancharatnam, Proc. Indian Acad. Sci. A44, 247 (1956)
12. H Poincaré, Theorie Mathematique de la Lumiere edited by George Carre (Paris, 1892) p. 275
13. G N Ramachandran and S Ramaseshan, Crystal optics in Handbuch der Physik (Springer, Berlin, 1961) vol. 25, part I
14. J Samuel and R Bhandari, Phys. Rev. Lett. 60, 2339 (1988)
15. R Bhandari, Phys. Lett. A180, 21 (1993)
16. P Hariharan, Hema Ramachandran, K S Suresh and J Samuel, The Pancharatnam phase as a strictly geometric phase: a demonstration using pure projections RRI-96-18, to appear in the J. Mod. Opt.
17. The definition of a ray here differs from [14, 3, 6], where only a phase and not the amplitude is 'modded out'. The present definition is the usual one in the mathematical literature
18. The case dim H = 1 is exceptional. In this case Δ is real and T does not determine χ. Either choice of χ is allowed. As a result there is an additional, discrete, two-fold ambiguity in the lift
19. V I Arnold, Mathematical methods of classical mechanics (Springer-Verlag, NY, 1978) Appendix 3
20. M C Abbati, R Cirelli, P Lanzavecchia and A Mania, Il Nuovo Cimento B83, 43 (1984)
21. V Cantoni and L Mistrangioli, Int. J. Theor. Phys. 31, 937 (1992)