A Canonical Relativistic Approach to Quantize Electromagnetic Field in the Presence of Moving Magneto-Dielectric Media

TL;DR

This paper develops a relativistic canonical framework to quantize electromagnetic fields in moving magneto-dielectric media, modeling the medium with a continuum of four vectors and deriving covariant equations for the system.

Contribution

It introduces a covariant quantization method for electromagnetic fields in moving media using a continuum model and derives new constitutive and noise polarization tensors.

Findings

Derived covariant wave and constitutive equations.

Expressed susceptibility tensor in terms of coupling tensor.

Calculated noise polarization tensor using the coupling tensor.

Abstract

A canonical relativistic formulation is introduced to quantize electromagnetic field in the presence of a polarizable and magnetizable moving medium. The medium is modeled by a continuum of four vectors in a phenomenological way. The covariant wave equation for the vector potential and the covariant constitutive equation of the medium are obtained as the Euler- Lagrange equations using the Lagrangian of the total system. A tensor of the third rank which couples the electromagnetic field with the medium is introduced and the susceptibility tensor of the medium is obtained in terms of the coupling tensor. Also the noise polarization tensor is calculated in terms of the coupling tensor and the creation and annihilation operators of the four vectors modeling the medium.