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Quantum statistical mechanical gauge invariance
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Quantum statistical mechanical gauge invariance
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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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Cited by 1 Pith paper
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Quantum statistical mechanics: Gauge invariance, operator shifting, hyperdensity functionals, and nonequilibrium sum rules
Extends gauge invariance via operator shifting in quantum statistical mechanics, deriving sum rules and hyperdensity functionals for equilibrium and nonequilibrium cases.
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