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Geometric Phase in General Relativity
Department of Physics, Bar Ilan University, Ramat Gan, Israel
School of Physics and Astronomy, Tel-Aviv University, Tel Aviv-Yafo, Israel
Department of Physics, Ariel University at the Shomron, Shomron, Israel
- 1 Department of Physics, Bar Ilan University, Ramat Gan, Israel
- 2 School of Physics and Astronomy, Tel-Aviv University, Tel Aviv-Yafo, Israel
- 3 Department of Physics, Ariel University at the Shomron, Shomron, Israel
Journal of Modern Physics·Volume 13 (2022)·Pages 1267–1271·Published 30 August 2022·DOI10.4236/jmp.2022.139075
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Abstract
We study the transport of a small wave packet in the embedding of the Stueckelberg-Horwitz-Piron relativistic quantum theory into the manifold of general relativity around the Schwarzschild solution using a semiclassical approximation. We find that the parallel transport of the momentum leads to a geometrical (Berry type) phase.
KeywordsGeometrical PhaseQuantum Theory in General RelativitySchwarzschild Solution
- Berry, M.V. (1984) Proceedings of the Royal Society A, 392, 45-57. https://doi.org/10.1098/rspa.1984.0023
- Weinberg, S. (1972) Gravitation and Cosmology, Principles and Applications of the General Theory of Relativity. John Wiley & Sons, Inc., Hoboken, p. 336.
- Thompson, R. and Rapini, G. (1993) Berry’s Phase and Gravitational Waves. Proceeding of the 5th Canadian Conference on General Relativity and Relativistic Astrophysics, Singapore, 13-15 May 1883.
- Sakurai, J.J. (2005) Modern Quantum Mechanics. Addison-Wesley, New York.
- Resta, R. (2000) Journal of Physics: Condensed Matter, 12, R107. https://doi.org/10.1088/0953-8984/12/9/201
- Horwitz, L.P. (2019) The European Physical Journal Plus, 134, 313. https://doi.org/10.1140/epjp/i2019-12689-7
- Chang, M.-C. and Niu, Q. (2008) Journal of Physics: Condensed Matter, 20, Article ID: 193202. https://doi.org/10.1088/0953-8984/20/19/193202
- Venturi, G. (1990) Quantum Gravity and the Berry Phase. In: Differential Geometric Methods in Theoretical Physics, Springer, New York, 703-713. https://doi.org/10.1007/978-1-4684-9148-7_69
- Mukhopadhyay, B. and Kanti Ganguly, S. (2020) Universe, 160, Article ID: 6100160. https://doi.org/10.3390/universe6100160
- Stone, M., Dwivedi, V. and Zlou, T. (2015) Physical Review D, 91, Article ID: 025004. https://doi.org/10.1103/PhysRevD.91.025004
- Ghosh, T. and Mukhopadhyay, B. (2020) International Journal of Modern Physics D, 30, Article ID: 2150090. https://doi.org/10.1142/S0218271821500905
- Ludwin, D.M. and Horwitz, L.P. (2011) Journal of Mathematical Physics, 52, Article ID: 012303. https://doi.org/10.1063/1.3533399
- Aharonov, Y. and Bohm, D. (1959) Physical Review, 115, 485. https://doi.org/10.1103/PhysRev.115.485