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 $\text{d}F=0$ (or $F=\text{d}A$) and $\text{d}H=J$ and a constitutive law $H = # F$ 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 are 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.

34 pages, references added, update to published version, title updated to published version

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• Teleparallel Palatini theories
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• Propagation of gravitational waves in teleparallel gravity theories
• Geodesics and the magnitude-redshift relation on cosmologically symmetric Finsler spacetimes
• Curved spacetimes with local $\kappa$-Poincaré dispersion relation
• On Kottler's path: origin and evolution of the premetric program in gravity and in electrodynamics
• An axiomatic purification of gravity
• Observers' measurements in premetric electrodynamics I: Time and radar length
• Quantum Energy Inequalities in Pre-Metric Electrodynamics
• Gravitational closure of matter field equations
• Electromagnetic analogue space-times, analytically and algebraically
• Inequalities from Lorentz-Finsler norms