Quantization of general linear electrodynamics

TL;DR

This paper develops a Hamiltonian formulation and quantization of general linear electrodynamics, revealing how the constitutive tensor influences quantum vacuum phenomena like the Casimir effect in bi-refringent media.

Contribution

It introduces a Hamiltonian framework for general linear electrodynamics and demonstrates how to quantize it, connecting classical constitutive relations to quantum vacuum effects.

Findings

Quantum vacuum depends on the constitutive tensor

Casimir effect calculated for bi-refringent media

Hamiltonian formulation derived from first principles

Abstract

General linear electrodynamics allow for an arbitrary linear constitutive relation between the field strength two-form and induction two-form density if crucial hyperbolicity and energy conditions are satisfied, which render the theory predictive and physically interpretable. Taking into account the higher-order polynomial dispersion relation and associated causal structure of general linear electrodynamics, we carefully develop its Hamiltonian formulation from first principles. Canonical quantization of the resulting constrained system then results in a quantum vacuum which is sensitive to the constitutive tensor of the classical theory. As an application we calculate the Casimir effect in a bi-refringent linear optical medium.