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  • Letter
  • Open Access

Quantum statistical mechanical gauge invariance

Johanna Müller and Matthias Schmidt*

  • *Contact author: Matthias.Schmidt@uni-bayreuth.de
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Phys. Rev. E 114, L022104 – Published 14 August, 2026

DOI: https://doi.org/10.1103/dzz3-m28k

Abstract

We address gauge invariance in the statistical mechanics of quantum many-body systems. The gauge transformation acts on the position and momentum degrees of freedom, and it is represented by a quantum shifting superoperator that maps quantum observables onto each other. The shifting superoperator is anti-self-adjoint, and it has noncommutative Lie algebra structure. These properties induce exact equilibrium sum rules that connect locally resolved force and hyperforce densities for any given observable. We argue that the framework is amenable to tight integration into quantum hyperdensity functional theory and that it generalizes naturally to nonequilibrium.

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Physics Subject Headings (PhySH)

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Quantum statistical mechanics: Gauge invariance, operator shifting, hyperdensity functionals, and nonequilibrium sum rules

Johanna Müller and Matthias Schmidt
Phys. Rev. E 114, 024130 (2026)

Article Text

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Outline

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Phys. Rev. E 114, L022104– Published 14 August, 2026
  • Received 24 September 2025
  • Revised 23 May 2026
  • Accepted 24 July 2026
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