On the path integral treatment for an Aharonov-Bohm field on the hyperbolic plane

International Journal of Theoretical Physics

Volumn 38, Issue 3, 1999, Pages 955-969

  Grosche, Christian ^a  

^a UNIVERSITY OF HAMBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033096275     PISSN: 00207748     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1026629607510     Document Type: Article

References (42)

1. Abramowitz, M., and Stegun, I. A., eds. (1984). Pocketbook of Mathematical Functions, Harry Deutsch, Frankfurt/Main, Germany.
2. Aharonov, Y., and Bohm, D. (1959). Significance of electromagnetic potentials in the quantum theory, Phys. Rev. 115, 485-491.
3. Anandan, J. S., and Safko, J. L., eds. (1994). Quantum Coherence and Reality. Proceedings of the International Conference on Fundamental Aspects of Quantum Theory in Celebration of the 60th Birthday of Yakir Aharonov, World Scientific, Singapore.
4. Barut, A. O., Inomata, A., and Junker, G. (1990). Path integral treatment of the hydrogen atom in a curved space of constant curvature: II. Hyperbolic space, J. Phys. A: Math. Gen. 23, 1179-1190.
5. Bernido, C. C. (1993). Path integral treatment of the gravitational anyon in a uniform magnetic field, J. Phys. A: Math. Gen. 26, 5461-5471.
6. Bernido, C. C., and Inomata, A. (1980). Topological shifts in the Aharonov-Bohm effect, Phys. Lett. A 77, 394-396.
7. Berndio, C. C., and Inomata, A. (1981). Path integrals with a periodic constraint: The Aharonov-Bohm effect, J. Math. Phys. 22, 715-718.
8. Chetouani, L., Guechi, L., and Hammann, T. F. (1989). Exact path integral solution of the Coulomb plus Aharonov-Bohm potential, J. Math. Phys. 30, 655-658.
9. Comtet, A. (1987). On the Landau levels on the hyperbolic plane, Ann. Phys. (N. Y.) 173, 185-209.
10. Drǎgǎnascu, Gh. E., Campigotto, C., and Kibler, M. (1992). On a generalized Aharonov-Bohm plus Coulomb system, Phys. Lett. A 170, 339-343.
11. Fay, J. D. (1977). Fourier coefficients of the resolvent for a Fuchsian group, J. Reine Angew. Math. 293, 143-203.
12. Feynman, R. P., and Hibbs, A. (1965). Quantum Mechanics and Path Integrals, McGraw-Hill, New York.
13. Gamboa, J., and Rivelles, V. O. (1991). Quantum mechanics of relativistic particles in multiply connected space and the Aharanov-Bohm effect, J. Phys. A: Math. Gen. 24, L659-L666.
14. Gerry, C. C., and Singh, V. A. (1979). Feynman path-integral approach to the Aharonov-Bohm effect, Phys. Rev. D 20, 2550-2554.
15. Gerry, C. C., and Smith, V. A. (1982). On the experimental consequences of the winding numbers of the Aharonov-Bohm effect, Phys. Lett. A 92, 11-12.
16. Gerry, C. C, and Singh, V. A. (1983). Effects of topology in the Aharonov-Bohm effect, Nuovo Cimento B 73, 161-170.
17. Gradshteyn, I. S., and Ryzhik, I. M. (1980). Table of Integrals, Series, and Products, Academic Press, New York.
18. Grosche, C. (1988). The path integral on the Poincaré upper half-plane with a magnetic field and for the Morse potential, Ann. Phys. (N.Y.) 187, 110-134.
19. Grosche, C. (1990a). Path integration on the hyperbolic plane with a magnetic field, Ann. Phys. (N. Y.) 201, 258-284.
20. Grosche, C. ( 1990b). The path integral for the Kepler problem on the pseudosphere, Ann. Phys. (N.Y.) 204, 208-222.
21. Grosche, C. (1996). Path Integrals, Hyperbolic Spaces, and Selberg Trace Formulæ, World Scientific, Singapore.
22. Grosche, C., and Steiner, F. (1988). The path integral on the pseudosphere, Ann. Phys. (N.Y.) 182, 120-156.
23. Grosche, C., and Steiner, F. (1998). Handbook of Feynman Path Integrals, Springer, Berlin.
24. Grosche, C., Pogosyan, G. S., and Sissakian, A. N. (1996). Path-integral approach to superintegrable potentials on the two-dimensional hyperboloid, Phys. Part. Nucl. 27, 244-278.
25. Gutzwiller, M. C. (1991). Chaos in Classical and Quantum Mechanics, Springer, Berlin.
26. Hejhal, D. A. (1976). The Selberg Trace Formula for PSL(2, ℝ), Springer, Berlin.
27. Higgs, P. W. (1979). Dynamical symmetries in a spherical geometry, J. Phys. A: Math. Gen. 12, 309-323.
28. Hoang, L. V., and Giang, N. T. (1993). On the Green function for a hydrogen-like atom in the Dirac monopole field plus the Aharonov-Bohm field, J. Phys. A: Math. Gen. 26, 3333-3338.
29. Hoang, L. V., Hai, L. X., Komarov, L. I., and Romaova, T. S. (1992). Relativistic analogy of the Aharonov-Bohm effect in the presence of Coulomb field and magnetic charge, J. Phys. A: Math. Gen. 25, 6461-6469.
30. Izmest'ev, A. A., Pogosyan, G. S., Sissakian, A. N., and Winternitz, P. (1997). Contractions of Lie algebras and separation of variables. Two-dimensional hyperboloid, Int. J. Mod. Phys. 12, 53-61.
31. Kibler, M., and Campigotto, C. (1993). On a generalized Aharonov-Bohm plus oscillator system, Phys. Lett. A 181, 1-6.
32. Kibler, M., and Negadi, T. (1987). Motion of a particle in a Coulomb field plus Aharonov-Bohm potential, Phys. Lett. A 124, 42-46.
33. Kleinert, H. (1995). Path Integrals in Quantum Mechanics, Statistics and Polymer Physics, World Scientific, Singapore.
34. Kuperin, Yu. A., Romanov, R. V., and Rudin, H. E. (1944). Scattering on the hyperbolic plane in the Aharonov-Bohm gauge field, Lett. Math. Phys. 31, 271-278.
35. Liang, J. Q. (1988). Path integrals in multiply connected spaces and the Aharonov-Bohm interference, Physica B 151, 239-244.
36. Lin, D.-H. (1998). Path integral for a relativistic Aharonov-Bohm-Coulomb system, J. Phys. A: Math. Gen. 31, 4785-4793.
37. 2u + λu = 0 allows the complete separation of variables., Math. Sb. 27, 379-426 [in Russian].
38. Park, D. K., and Yoo, S.-K. (1998). Propagators for spinless and spin-1/2 Aharonov-Bohm-Coulomb systems, Ann. Phys. (N.Y.) 263, 295-309.
39. Peak, D., and Inomata, A. (1969). Summation over Feynman histories in polar coordinates, J. Math. Phys. 10, 1422-1428.
40. Pnueli, A. (1994). Scattering matrices and conductances of leaky tori, Ann. Phys. (N.Y.) 231, 56-83.
41. Schulman, L. S. (1971). Approximate topologies, J. Math. Phys. 12, 304-308.
42. Schulman, L. S. (1981). Techniques and Applications of Path Integration, Wiley, New York.