Feynman path integrals for discrete-variable systems: Walks on Hamiltonian graphs

• URL: http://arxiv.org/abs/2407.11231v1
• Date: Mon, 15 Jul 2024 20:44:02 GMT
• Title: Feynman path integrals for discrete-variable systems: Walks on Hamiltonian graphs
• Authors: Amir Kalev, Itay Hen,
• Abstract summary: 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. We explicitly recover Feynman's continuous-variable path integrals.
• Score: 0.46040036610482665
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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