Coherent-state path integrals in quantum thermodynamics, by Luca Salasnich, Cesare Vianello

SciPost Physics Lecture Notes Home Authoring Refereeing Submit a manuscript About Coherent-state path integrals in quantum thermodynamics Luca Salasnich, Cesare Vianello SciPost Phys. Lect. Notes 117 (2026) · published 18 February 2026 doi: 10.21468/SciPostPhysLectNotes.117 pdf BiBTeX RIS Submissions/Reports 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. × TY - JOURPB - SciPost FoundationDO - 10.21468/SciPostPhysLectNotes.117TI - Coherent-state path integrals in quantum thermodynamicsPY - 2026/02/18UR - https://scipost.org/SciPostPhysLectNotes.117JF - SciPost Physics Lecture NotesJA - SciPost Phys. Lect. NotesSP - 117A1 - Salasnich, LucaAU - Vianello, CesareAB - 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.ER - × @Article{10.21468/SciPostPhysLectNotes.117, title={{Coherent-state path integrals in quantum thermodynamics}}, author={Luca Salasnich and Cesare Vianello}, journal={SciPost Phys. Lect. Notes}, pages={117}, year={2026}, publisher={SciPost}, doi={10.21468/SciPostPhysLectNotes.117}, url={https://scipost.org/10.21468/SciPostPhysLectNotes.117},} Ontology / Topics See full Ontology or Topics database. Bogoliubov-de Gennes equations Bose-Einstein condensates (BECs) Euler hydrodynamics Fermi gases Finite-size corrections Hubbard model Quantum field theory (QFT) Quantum gases Superconductivity/superconductors Superfluidity Authors / Affiliations: mappings to Contributors and Organizations See all Organizations. 1 2 3 Luca Salasnich, 1 3 Cesare Vianello 1 Università degli Studi di Padova / University of Padua [UNIPD] 2 Istituto Nazionale di Ottica [INO] 3 INFN Sezione di Padova [INFN Padova] Funders for the research work leading to this publication Instituto Nazionale di Fisica Nucleare (INFN) (through Organization: Istituto Nazionale di Fisica Nucleare / National Institute for Nuclear Physics [INFN]) Ministero dell'Università e della Ricerca NextGenerationEU