Time-dependent Hilbert spaces, geometric phases, and general covariance in quantum mechanics

Physics Letters, Section A: General, Atomic and Solid State Physics

Volumn 320, Issue 5-6, 2004, Pages 375-382

  Mostafazadeh, Ali ^a  

^a KOÇ UNIVERSITY   (Turkey)

Author keywords

[No Author keywords available]

Indexed keywords

HAMILTONIANS; QUANTUM OPTICS; RELATIVITY; VECTOR SPACES;

DYNAMICAL INVARIANTS; GENERAL COVARIANCE; GENERAL RELATIVITY; GEOMETRIC PHASIS; POSITIVE DEFINITE; QUANTUM MECHANICAL; SYMMETRY GROUPS; TIME INDEPENDENTS;

HILBERT SPACES;

ARTICLE; COVARIANCE; GEOMETRY; MATHEMATICAL ANALYSIS; METRIC SYSTEM; PHYSICS; QUANTUM MECHANICS; QUANTUM THEORY; SPACE;

EID: 0346655336     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physleta.2003.12.008     Document Type: Article

References (25)

1. T.W.B. Kibble, Commun. Math. Phys. 65 (1979) 201; A. Ashtekar, T.A. Schilling, gr-qc/9706069; D.C. Brody, L.P. Hughston, J. Geom. Phys. 38 (2001) 19.
2. T.W.B. Kibble, Commun. Math. Phys. 65 (1979) 201; A. Ashtekar, T.A. Schilling, gr-qc/9706069; D.C. Brody, L.P. Hughston, J. Geom. Phys. 38 (2001) 19.
3. T.W.B. Kibble, Commun. Math. Phys. 65 (1979) 201; A. Ashtekar, T.A. Schilling, gr-qc/9706069; D.C. Brody, L.P. Hughston, J. Geom. Phys. 38 (2001) 19.
4. S. Weinberg, Ann. Phys. (N.Y.) 194 (1989) 336.
5. D. Minic, C.-H. Tze, hep-th/0305193.
6. A. Bohm, A. Mostafazadeh, H. Koizumi, Q. Niu, J. Zwanziger, The Geometric Phase in Quantum Systems, Springer, New York, 2003, see also [8].
7. R.M. Wald, General Relativity, University of Chicago Press, Chicago, 1984.
8. S. Carlip, Rep. Prog. Phys. 64 (2001) 885.
9. J.S. Anandan, in: R.S. Cohen, M. Horne, J. Stachel (Eds.), Potentiality, Entanglement and Passion-at-a-distance-Quantum Mechanical Studies for Abner Shimony, Vol. 2, Kluwer, Dordrecht, 1997.
10. A. Mostafazadeh, Dynamical Invariants, Adiabatic Approximation, and the Geometric Phase, Nova Science, New York, 2001.
11. K.-H. Yang, Ann. Phys. (N.Y.) 101 (1976) 62; D.H. Kobe, J. Phys. A: Math. Gen. 23 (1990) 4249.
12. K.-H. Yang, Ann. Phys. (N.Y.) 101 (1976) 62; D.H. Kobe, J. Phys. A: Math. Gen. 23 (1990) 4249.
13. F.G. Scholtz, H.B. Geyer, F.J.W. Hahne, Ann. Phys. 213 (1992) 74.
14. T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin, 1995.
15. M. Reed, B. Simon, Functional Analysis, Vol. I, Academic Press, San Diego, 1980.
16. N. Weaver, Mathematical Quantization, Chapman and Hall/CRC, Boca Raton, FL, 2001.
17. P. Seba, Phys. Rev. A 41 (1990) 2306.
18. C.J. Isham, in: L.A. Ibort, M.A. Ropdriguez (Eds.), Integrable Systems, Quantum Groups, and Quantum Field Theories, Kluwer, Dordrecht, 1993.
19. P. Pereshogin, P. Pronin, Phys. Lett. A 156 (1991) 12.
20. A. Mostafazadeh, Class. Quantum Grav. 20 (2003) 155, see also [19].
21. H.R. Lewis Jr., W.B. Riesenfeld, J. Math. Phys. 10 (1969) 1458.
22. A. Mostafazadeh, Ann. Phys. (N.Y.) 309 (2004) 1.
23. A. Mostafazadeh, J. Phys. A: Math. Gen. 34 (2001) 6325.
24. G. Lindblad, Commun. Math. Phys. 48 (1976) 119.
25. R.A. Bertlmann, W. Grimus, Phys. Lett. A 300 (2002) 107.