Phase operator of the quantum supersymmetric harmonic oscillator

TL;DR

This paper introduces and analyzes the phase operator for quantum fermionic and supersymmetric harmonic oscillators, revealing its role as a Goldstone operator at any positive temperature, thus advancing understanding of quantum symmetries.

Contribution

It is the first to define and explore the phase operator in quantum supersymmetric harmonic oscillators, highlighting its Goldstone nature at finite temperatures.

Findings

Phase operator defined for fermionic and supersymmetric oscillators

The phase operator acts as a Goldstone operator at positive temperatures

Provides new insights into quantum symmetry breaking at finite temperatures

Abstract

After a brief introduction recalling how, in the limit in which the mass and the electric charge of the electron and the positron tend to zero, Quantum Electrodynamics reduces to a collection of uncoupled quantum supersymmetric harmonic oscillators, the phase operator of the quantum fermionic harmonic oscillator and of the quantum supersymmetric harmonic oscillator are introduced and their properties analyzed. It is then shown that the phase operator of a supersymmetric harmonic oscillator is a Goldstone operator at any strictly positive temperature (finite or infinite).