Superoperator transformation theory in quantum mechanics

Fan, Hong-Yi, H. Hu +1 more

Russell Davidson, John Rae

The superoperator transformation theory developed by the Brussels school is applied to a simple quantum-mechanical system : the one-boson Lee model. The existence of a diagonalising transformation for this model permits the solution of dynamical problems such as that of induced emission and the construction of explicit matrix representations for asymptotic and dressing operators of the theory.

P. Cordero, Sergio A. Hojman

J Rae

The superoperator theory of nonequilibrium statistical mechanics is applied to the Dirac and Klein-Gordon equations. The transformation operators of this theory are found to be closely related to the Foldy-Wouthuysen transformation while the associated subdynamics corresponds to the separation into smooth motion and zitterbewegung.

Anonymous, Matthias Schmidt

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.