Feynman path integrals on compact Lie groups with bi-invariant Riemannian metrics
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866915466791878656 |
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| author | Drago, Nicoló Mazzucchi, Sonia Moretti, Valter |
| author_facet | Drago, Nicoló Mazzucchi, Sonia Moretti, Valter |
| contents | In this work we consider a suitable generalization of the Feynman path integral on a specific class of Riemannian manifolds consisting of compact Lie groups with bi-invariant Riemannian metrics. The main tools we use are the Cartan development map, the notion of oscillatory integral, and the Chernoff approximation theorem. We prove that, for a class of functions of a dense subspace of the relevant Hilbert space, the Feynman map produces the solution of the Schrödinger equation, where the Laplace-Beltrami operator coincides with the second order Casimir operator of the group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_03282 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Feynman path integrals on compact Lie groups with bi-invariant Riemannian metrics Drago, Nicoló Mazzucchi, Sonia Moretti, Valter Mathematical Physics Functional Analysis Probability In this work we consider a suitable generalization of the Feynman path integral on a specific class of Riemannian manifolds consisting of compact Lie groups with bi-invariant Riemannian metrics. The main tools we use are the Cartan development map, the notion of oscillatory integral, and the Chernoff approximation theorem. We prove that, for a class of functions of a dense subspace of the relevant Hilbert space, the Feynman map produces the solution of the Schrödinger equation, where the Laplace-Beltrami operator coincides with the second order Casimir operator of the group. |
| title | Feynman path integrals on compact Lie groups with bi-invariant Riemannian metrics |
| topic | Mathematical Physics Functional Analysis Probability |
| url | https://arxiv.org/abs/2307.03282 |