Work

Coherent-state path integrals in quantum thermodynamics

Year: 2026

Type: article

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.

Source: SciPost Physics Lecture Notes

DOI: 10.21468/scipostphyslectnotes.117

Authors: Luca Salasnich, Cesare Vianello

Institutions: University of Padua, Istituto Nazionale di Fisica Nucleare, Sezione di Padova, National Institute of Optics

Language: English

Topic: Quantum many-body systems

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

Funders: Dipartimenti di Eccellenza, European Commission, Ministero dell'Università e della Ricerca, NextGenerationEU

Award: G1605908383