Gauge transformation of quantum states in probability representation

TL;DR

This paper explores gauge invariance in quantum state probability representations, providing explicit transformations and introducing gauge-independent distributions with classical-limit evolution equations.

Contribution

It presents explicit gauge transformation formulas for quantum tomograms and introduces gauge-independent distributions with classical-limit evolution equations.

Findings

Explicit gauge transformation expressions for quantum tomograms

Introduction of gauge-independent optical and symplectic distributions

Evolution equations reduce to classical Liouville form in the classical limit

Abstract

The gauge invariance of the evolution equations of tomographic probability distribution functions of quantum particles in an electromagnetic field is illustrated. Explicit expressions for the transformations of ordinary tomograms of states under a gauge transformation of electromagnetic field potentials are obtained. Gauge-independent optical and symplectic tomographic quasi-distributions and tomographic probability distributions of states of quantum system are introduced, and their evolution equations having the Liouville equation in corresponding representations as the classical limit are found.