Prequantisation from the path integral viewpoint
Abstract
The quantum mechanically admissible definitions of the factor $\exp\big[(i/\hbar)S(\gamma)\big]$ in the Feynman integral are put in bijection with the prequantisations of Kostant and Souriau. The different allowed expressions of this factor -- the inequivalent prequantisations -- are classified. The theory is illustrated by the Aharonov-Bohm experiment and by identical particles.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2024
- DOI:
- 10.48550/arXiv.2402.17629
- arXiv:
- arXiv:2402.17629
- Bibcode:
- 2024arXiv240217629H
- Keywords:
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- Mathematical Physics;
- Quantum Physics
- E-Print:
- This note is the slightly reworded, rearranged and extended version of one originally published in the Proceedings of the {\sl Int. Conf. on Diff. Geom. Meths. in Math. Phys.}, Clausthal'1980, Doebner (ed). Springer Lecture Notes in Math. \textbf{905}, p.197-206 (1982). Marseille preprint CPT-80-P-1230. 14 pages, 2 figures