Boundaries and junctions in two parity violating models in 2+1 dimensions

TL;DR

This paper investigates boundary behaviors and junctions in two parity-violating models in 2+1 dimensions, revealing how gauge invariance influences interface dynamics, modifies electrodynamics, and affects wave dispersion and optical activity.

Contribution

It introduces a gauge-invariant approach to interface behavior in parity-violating models, extending Maxwell-Chern-Simons theory and analyzing wave dispersion and optical effects.

Findings

Gauge invariance determines interface behavior.

Modified electrodynamics at boundaries.

Optical activity and Faraday effect observed.

Abstract

Recently it has been suggested that junctions between materials with different parity violating properties would be characterized by diffusion layers, analogous to those in the p-n junction. This remark is amplified by a fuller investigation of two related parity violating effective Lagrangians, which possess a kind of duality. It is shown that gauge invariance and energy conservation are sufficient to determine the behaviour at the interface. This leads to modifications of normal parity-violating electrodynamics. The coupling of an interface to an external system is a natural solution to the deficiencies of Maxwell-Chern-Simons theory. A heuristic model of a transistor-like device is discussed which relates to recent experiments in device technology. Radiative corrections to Chern-Simons theory induce a local magnetic moment interaction whose lagrangian is everywhere gauge invariant. The effects of this interaction are compared to Maxwell-Chern-Simons theory. The dispersion of classical waves for these models is computed and the laws of reflection and refraction are found to hold despite the lack of $P$ and $T$ invariance. The magnetic moment dispersion is gapless in contrast to the Chern-Simons dispersion except in the case of a scalar field which is covariantly constant. Both models exhibit optical activity (Faraday effect).