Topological and geometrical phases due to gravitational field with curvature and torsion. (English) Zbl 0941.81539
Summary: The gravitational phase factor, which may be used to determine the evolution of a wave function in the WKB approximation, is modified to incorporate the Fermi-Walker transport of the wave function when it is accelerated, for example by a wave guide. The modified phase factor is used to obtain geometrical and topological phases in the interference of two coherent beams around a cosmic string containing mass and intrinsic spin. An exact solution for the string from the Einstein-Cartan-Sciama-Kibble gravitational field equations is used to interpret the topological phases as being due to the fluxes of curvature and torsion inside the string.
MSC:
| 81Q20 | Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory |
| 83C47 | Methods of quantum field theory in general relativity and gravitational theory |
References:
| [1] | Vilenkin, A., Phys. Rev. D, 23, 852 (1981) |
| [2] | Kibble, T. W.B., J. Math. Phys., 2, 212 (1961) · Zbl 0095.22903 |
| [3] | Wisnievsky, D.; Aharonov, Y., Ann. Phys., 45, 479 (1967) |
| [4] | Anandan, J., Nuovo Cimento, 53A, 221 (1979) |
| [5] | Greenberger, D.; Overhauser, A. W., Rev. Mod. Phys., 51, 43 (1979) |
| [6] | Wu, T. T.; Yang, C. N., Phys. Rev. D, 12, 3845 (1975) |
| [7] | Anandan, J., (Denardo, G.; Doebner, H. D., Conference on differential geometric methods in physics (1983), World Scientific: World Scientific Singapore), 211 |
| [8] | Anandan, J., Phys. Rev. D, 33, 2280 (1986) |
| [9] | Anandan, J., (Marlow, A. R., Quantum theory and gravitation (1980), Academic Press: Academic Press New York), 157 |
| [10] | Yang, C. N., Phys. Rev. Lett., 33, 445 (1974) · Zbl 1329.81278 |
| [11] | Bargmann, V.; Wigner, E., Proc. Nat. Acad. Sci., 34, 211 (1948) · Zbl 0030.42306 |
| [12] | Ann. Inst. Henri Poincaré, 49, 271 (1988) |
| [13] | Anandan, J.; Lesche, B., Lett. Nuovo Cimento, 37, 391 (1983) |
| [14] | Rauch, H.; Treimer, W.; Bonse, U., Phys. Lett. A, 47, 369 (1974) |
| [15] | Misner, C. W.; Thorne, K. S.; Wheeler, J. A., Gravitation, ((1973), Freeman: Freeman San Francisco), 175 |
| [16] | Trautman, A., (Mehra, J., The physicist’s conception of nature (1973), Reidel: Reidel Dordrecht) |
| [17] | Anandan, J., (Hu, B. L.; Ryan, M. P.; Vishveshwara, C. V., Papers in honor of Charles Misner. Papers in honor of Charles Misner, Directions in general relativity, Vol. 1 (1993), Cambridge Univ. Press: Cambridge Univ. Press Cambridge) |
| [18] | Deser, S.; Jackiw, R.; ’t Hooft, G., Ann. Phys. (NY), 152, 220 (1984) |
| [19] | Mazur, P. O., Phys. Rev. Lett., 59, 2380 (1987) |
| [20] | Arkuszewski, W.; Kopczynski, W.; Ponomariev, V. N., Commun. Math. Phys., 45, 183 (1975) |
| [21] | Anandan, J., Quantum coherence and reality, (Anandan, J. S.; Safko, J. L., Proc. Conf. on Fundamental aspects of quantum theory. Proc. Conf. on Fundamental aspects of quantum theory, Columbia, SC (1992), World Scientific: World Scientific Singapore), 1994 · Zbl 0941.81539 |
| [22] | Tsoubelis, D., Phys. Rev. Lett., 51, 2235 (1983) |
| [23] | Gott, J. R., Astrophys. J., 288, 422 (1985) |
| [24] | Hiscock, W. A., Phys. Rev. D, 31, 3288 (1985) |
| [25] | Tod, K. P., Class. Quantum Grav., 11, 1331 (1994) · Zbl 0798.53081 |
| [26] | Anandan, J., Phys. Rev. D, 15, 1448 (1977) |
| [27] | Anandan, J., Gen. Relat. Grav., 26, 125 (1994) |
| [28] | Anandan, J., Phys. Rev. Lett., 48, 1660 (1982) |
| [29] | Aharonov, Y.; Casher, A., Phys. Rev. Lett., 53, 319 (1984) |
| [30] | Anandan, J., Found. Phys., 10, 601 (1980) |
| [31] | Soleng, H. H., Gen. Relat. Grav., 24, 111 (1992) · Zbl 0753.35114 |
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