Feynman path integrals for discrete-variable systems: Walks on Hamiltonian graphs
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911302749782016 |
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| author | Kalev, Amir Hen, Itay |
| author_facet | Kalev, Amir Hen, Itay |
| contents | We propose a natural, parameter-free, discrete-variable formulation of Feynman path integrals. We show that for discrete-variable quantum systems, Feynman path integrals take the form of walks on the graph whose weighted adjacency matrix is the Hamiltonian. By working out expressions for the partition function and transition amplitudes of discretized versions of continuous-variable quantum systems, and then taking the continuum limit, we explicitly recover Feynman's continuous-variable path integrals. We also discuss the implications of our result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_11231 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Feynman path integrals for discrete-variable systems: Walks on Hamiltonian graphs Kalev, Amir Hen, Itay Quantum Physics Statistical Mechanics We propose a natural, parameter-free, discrete-variable formulation of Feynman path integrals. We show that for discrete-variable quantum systems, Feynman path integrals take the form of walks on the graph whose weighted adjacency matrix is the Hamiltonian. By working out expressions for the partition function and transition amplitudes of discretized versions of continuous-variable quantum systems, and then taking the continuum limit, we explicitly recover Feynman's continuous-variable path integrals. We also discuss the implications of our result. |
| title | Feynman path integrals for discrete-variable systems: Walks on Hamiltonian graphs |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2407.11231 |