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Coherent-state path integrals in quantum thermodynamics
by Luca Salasnich, Cesare Vianello
Submission summary
| Authors (as registered SciPost users): | Luca Salasnich · Cesare Vianello |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2511.11547v1 (pdf) |
| Date submitted: | Nov. 17, 2025, 4:47 p.m. |
| Submitted by: | Luca Salasnich |
| Submitted to: | SciPost Physics Lecture Notes |
| Ontological classification | |
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| Academic field: | Physics |
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| Approach: | Theoretical |
Abstract
In these notes, we elucidate some subtle aspects of coherent-state path integrals, focusing on their application to the equilibrium thermodynamics of quantum many-particle systems. These subtleties emerge when evaluating path integrals in the continuum, either in imaginary time or in Matsubara-frequency space. Our central message is that, when handled with due care, the path integral yields results identical to those obtained from the canonical Hamiltonian approach. We illustrate this through a pedagogical treatment of several paradigmatic systems: the bosonic and fermionic harmonic oscillators, the single-site Bose-Hubbard and Hubbard models, the weakly-interacting Bose gas with contact and finite-range interactions, and the BCS superconductor with contact and finite-range interactions.
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