Quantum statistical mechanics: Gauge invariance, operator shifting, hyperdensity functionals, and nonequilibrium sum rules (opens in new tab)

We provide an extended acount of the recent statistical mechanical theory of gauge invariance against operator shifting in quantum many-body systems (arXiv:2509.20494). The gauge transformation is enacted by a shifting superoperator that displaces the fundamental position and momentum degrees of freedom. The shifting superoperator constitutes a map between Hilbert space operators and it features Lie algebra commutator structure. Averages of gene...