Electromagnetic potential in pre-metric electrodynamics: Causal structure, propagators and quantization

Abstract

An axiomatic approach to electrodynamics reveals that Maxwell electrodynamics is just one instance of a variety of theories for which the name electrodynamics is justified. They all have in common that their fundamental input are Maxwell's equations dF ¼ 0 (or F ¼ dA) and dH ¼ J and a constitutive law H ¼ #F which relates the field strength two-form F and the excitation two-form H. A local and linear constitutive law defines what is called local and linear pre-metric electrodynamics whose best known application is the effective description of electrodynamics inside media including, e.g., birefringence. We analyze the classical theory of the electromagnetic potential A before we use methods familiar from mathematical quantum field theory in curved spacetimes to quantize it in a locally covariant way. Our analysis of the classical theory contains the derivation of retarded and advanced propagators, the analysis of the causal structure on the basis of the constitutive law (instead of a metric) and a discussion of the classical phase space. This classical analysis sets the stage for the construction of the quantum field algebra and quantum states. Here one sees, among other things, that a microlocal spectrum condition can be formulated in this more general setting.

Propagation of gravitational waves in teleparallel gravity theories

“…In order to derive the principal symbol we must restrict the field equations to the subspace of fields, on which they are non-degenerate. This feature is common in field theories with gauge degrees of freedom and appears also in general premetric theories of electrodynamics [43].…”

Teleparallel theories of gravity as analogue of nonlinear electrodynamics

“…with |g| = | det g ab |. Electrodynamics in media, like in an uniaxial birefringent crystal for example [38,39], is described by the constitutive density…”

“…where X is the spacelike direction of the optical axis of the crystal and U the timelike direction which characterizes the rest frame of the crystal. Recently local and linear premetric electrodynamics has gained some interest as model for a quantum field theory based on a more general causal structure than that of a Lorentzian metric [39][40][41][42].…”

Observers’ measurements in premetric electrodynamics: Time and radar length

“…(3) by contraction with the total antisymmetric Levi-Civita symbol ϵ abcd , which is normalized such that ϵ 0123 = 1. The covariant formulation of premetric electrodynamics enables a precise study of the propagation behaviour of light in this general setting [24] and for the quantization of the theory [14,25,26]. General premetric electrodynamics covers a huge variety of effects.…”