Coherent-state path integrals in quantum thermodynamics

Luca Salasnich; Cesare Vianello

doi:10.21468/scipostphyslectnotes.117

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arXiv · 2511.11547

Coherent-state path integrals in quantum thermodynamics

Luca Salasnich·Cesare Vianello

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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 finite-range interactions, and the BCS superconductor with finite-range interactions.

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Luca Salasnich, Cesare Vianello. 2025-11-14. Coherent-state path integrals in quantum thermodynamics. https://doi.org/10.21468/scipostphyslectnotes.117

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