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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 9: Quantenfeldtheorie II
MP 9.2: Talk
Thursday, March 3, 2016, 14:05–14:25, VMP6 HS B
The Potential in General Linear Electrodynamics: Causal Structure, Propagators and Quantization — •Daniel Siemssen1 and Christian Pfeifer2,3 — 1Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw — 2Institute for Theoretical Physics, Leibniz Universität Hannover — 3Center of Applied Space Technology and Microgravity (ZARM), Universität Bremen
From an axiomatic point of view, the fundamental input for a theory of electrodynamics are Maxwell’s equations dF=0 (or F=dA) and dH=J, and a constitutive law H=# F, which relates the field strength 2-form F and the excitation 2-form H. In this talk we consider general linear electrodynamics, the theory of electrodynamics defined by a linear constitutive law. The best known application of this theory is the effective description of electrodynamics inside (linear) media (e.g. birefringence). We will 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. 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, including a (generalized) microlocal spectrum condition.