Quantum statistical mechanical gauge invariance
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.
Fields of Study & Subjects
Statistical Mechanics and Entropy
Advanced Thermodynamics and Statistical Mechanics
Quantum Information and Cryptography
Publication details
- Journal / source
- Physical review. E
- Publisher
- American Physical Society (APS)
- Volume
- 114
- Issue
- 2
- Publication date
- 24 July 2026
- Language
- EN