Special Relativity in Quantum Phase Space

TL;DR

This paper develops a phase space approach to special relativity in quantum systems, showing how relativistic transformations distort quantum phase space distributions similarly to optical aberrations.

Contribution

It introduces a relativistic phase space framework for quantum particles, highlighting how Lorentz transformations affect quantum localization and phase space distributions.

Findings

Quantum localization remains finite under inertial transformations.

Relativistic transformations distort phase space distributions akin to optical aberrations.

The approach bridges quantum mechanics and special relativity in phase space.

Abstract

A phase space treatment of special relativity of quantum systems is developed. In this approach a quantum particle remains localized if subject to inertial transformations, the localization occurring in a finite phase space area. Unlike non-relativistic transformations, relativistic transformations generally distort the phase space distribution function, being equivalent to aberrations in optics.