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A Path Integral for Spin
Abstract
A path integral for spinning particles is developed. It is a one-particle theory, equivalent to the usual quantum mechanics. Our method employs a classical model for spin which is quantized by path integration. The model, the spherical top, is a natural one from a group-theoretic point of view and has been used before in a similar context. The curvature and multiple connectedness of the top coordinate space [$\mathrm{SO}(3)$] provide some interesting features in the sum over paths. The Green's function which results from this procedure propagates all spins, and recovery of the usual Pauli spinors from this formalism is achieved by projection to a specific spin subspace.
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Citations
Cited by
Constraints imposed byCPconservation in the presence of pseudoparticles
Peccei, R. D., & Quinn, H. R. (1977) · Physical Review D · doi:10.1103/physrevd.16.1791 · Cited by 3,148
Particle spin dynamics as the grassmann variant of classical mechanics
Berezin, F. A., & Marinov, M. S. (1977) · Annals of Physics · doi:10.1016/0003-4916(77)90335-9 · Cited by 769
General Theory for Quantum Statistics in Two Dimensions
Wu, Y.-S. (1984) · Physical Review Letters · doi:10.1103/physrevlett.52.2103 · Cited by 434
Solution of the Schrödinger equation in terms of classical paths
Balian, R., & Bloch, C. (1974) · Annals of Physics · doi:10.1016/0003-4916(74)90421-7 · Cited by 381
The relativistic spherical top
Hanson, A. J., & Regge, T. (1974) · Annals of Physics · doi:10.1016/0003-4916(74)90046-3 · Cited by 338
Metadata
- Authors
- Schulman, L.
- Venue
- Physical Review
- Publisher
- American Physical Society (APS)
- Published
- 1968-12-25
- Volume
- 176
- Issue
- 5
- Pages
- 1558-1569
- ISSN
- 0031-899X (ISSN-L)
- OpenAlex
- W2061971595
- Cited by
- 328
- References
- 0
- FWCI
- 2.93
- Type
- journal article
- Language
- en
- Open access
- closed
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- Schulman, L. (1968). A Path Integral for Spin. Physical Review. https://doi.org/10.1103/physrev.176.1558
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