Propagation of photons and massive vector mesons between a parity breaking medium and vacuum

TL;DR

This paper investigates how photons and massive vector mesons propagate across a boundary between a parity-violating medium and vacuum, analyzing transmission, reflection, and propagators with implications for detecting local parity violation.

Contribution

It provides a detailed analysis of particle propagation in parity-odd media, including classical solutions, quantum formalism, and boundary effects, which was not comprehensively addressed before.

Findings

Calculated transmission and reflection probabilities for different polarizations.

Derived the propagator for particles in the presence of a parity-breaking boundary.

Identified the significance of boundary effects for detecting local parity violation.

Abstract

The problem of propagation of photons and massive vector mesons in the presence of Lorenz and CPT invariance violating medium is studied when the parity-odd medium is bounded by a hyperplane separating it from the vacuum. The solutions in both half-spaces are carefully discussed and in the case of space-like boundary stitched on the boundary with help of the Bogolubov transformations provided by the space-like Chern-Simons vector. The presence of two different Fock vacua is shown and the probability amplitude for transmission of particles from vacuum to parity breaking medium is calculated. We have also found classical solutions and showed that the results are consistent with ones obtained by canonical quantization formalism. In the cases, both of entrance to and of escaping from parity-odd medium, the probabilities for reflecting and passing through were found for each polarization using the classical solutions. Finally, the propagator for each polarization is obtained in the momentum space. Boundary effects under consideration are of certain importance for registration of local parity violation in the finite volume of heavy ion fireball and/or of a star with cold axion condensate.