Parity Breaking Medium and Squeeze Operators

TL;DR

This paper explores the quantum field behavior at the boundary between Minkowski space and a parity-breaking medium, deriving algebraic structures and probabilities for particle pair production and transmission.

Contribution

It introduces an algebraic framework involving Bogolyubov transformations and squeezed states to analyze boundary effects in parity-breaking media.

Findings

Derived SU(2) algebra from squeezed states

Calculated reflection and transmission probabilities

Generalized pair production rate formula

Abstract

The transition between a Minkowski space region and a parity breaking medium domain is thoroughly discussed. The requirement of continuity of the field operator content across the separating boundary of the two domains leads to Bogolyubov transformations, squeezed pairs states and squeeze operators that turn out to generate a functional SU(2) algebra. According to this algebraic approach, the reflection and transmission probability amplitude across the separating boundary are computed. The probability rate of the emission or absorption of squeezed pairs out of the vacuum (generalization of the Sauter-Schwinger-Nikishov formula) is obtained.