A Derivation of Geometric Quantization via Feynman's Path Integral on Phase Space
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929360257155072 |
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| author | Lackman, Joshua |
| author_facet | Lackman, Joshua |
| contents | We derive the geometric quantization program of symplectic manifolds, in the sense of both Kostant-Souriau and Weinstein, from Feynman's path integral formulation on phase space. The state space we use contains states with negative norm and polarized sections determine a Hilbert space. We discuss ambiguities in the definition of path integrals arising from the distinct Riemann sum prescriptions and its consequence on the quantization of symplectomorphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_17273 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Derivation of Geometric Quantization via Feynman's Path Integral on Phase Space Lackman, Joshua Symplectic Geometry High Energy Physics - Theory Mathematical Physics Quantum Algebra We derive the geometric quantization program of symplectic manifolds, in the sense of both Kostant-Souriau and Weinstein, from Feynman's path integral formulation on phase space. The state space we use contains states with negative norm and polarized sections determine a Hilbert space. We discuss ambiguities in the definition of path integrals arising from the distinct Riemann sum prescriptions and its consequence on the quantization of symplectomorphisms. |
| title | A Derivation of Geometric Quantization via Feynman's Path Integral on Phase Space |
| topic | Symplectic Geometry High Energy Physics - Theory Mathematical Physics Quantum Algebra |
| url | https://arxiv.org/abs/2405.17273 |