Gauge Invariant Quantization of Dissipative Systems of Charged Particles in Extended Phase Space

TL;DR

This paper demonstrates that the extended phase space formulation of quantum mechanics restores gauge invariance in the conductivity of dissipative charged particle systems under external electric fields, unifying different gauge solutions.

Contribution

It extends the phase space approach to show gauge invariance in dissipative quantum systems, resolving discrepancies from previous gauge-dependent solutions.

Findings

Both gauges yield the same conductivity, confirming gauge invariance.

Extended phase space approach unifies different gauge solutions.

Demonstrates the effectiveness of the formalism for dissipative systems.

Abstract

Recently, it is shown that the extended phase space formulation of quantum mechanics is a suitable technique for studying the quantum dissipative systems. Here, as a further application of this formalism, we consider a dissipative system of charged particles interacting with an external time dependent electric field. Such a system has been investigated by Buch and Denman, and two distinct solutions with completely different structure have been obtained for Schr\"odinger's equation in two different gauges. However, by generalizing the gauge transformations to the phase space and using the extended phase space technique to study the same system, we demonstrate how both gauges lead to the same conductivity, suggesting the recovery of gauge invariance for this physical quantity within the extended phase space approach.