Quantization of general linear electrodynamics

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.

23 pages, 1 figure

References in corpus (8)

• General Very Special Relativity is Finsler Geometry
• String Quantum Gravity, Lorentz-Invariance Violation and Gamma-Ray Astronomy
• Lorentz Invariance Violation and Symmetry in Randers--Finsler Spaces
• The Higgs mechanism in Finsler spacetimes
• Propagation of light in area metric backgrounds
• The non-birefringent limit of all linear, skewonless media and its unique light-cone structure
• Modified Dispersion Relations from the Renormalization Group of Gravity
• A note on particle kinematics in Horava-Lifshitz scenarios