Microlocal methods in quantum field theory

by Arne Hofmann
Doctoral thesis
Date of Examination:2023-12-15
Date of issue:2024-11-14
Advisor:Prof. Dr. Dorothea Bahns
Referee:Prof. Dr. Dorothea Bahns
Referee:Prof. Dr. Ingo Witt
Persistent Address: http://dx.doi.org/10.53846/goediss-10857

 

 

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Abstract

English

The renormalisation of Feynman diagrams is considered in the context of perturbative algebraic quantum field theory. The construction of Wick polynomials is related to the renormalisation of diagrams with short loops (tadpoles). Microlocal techniques are used to prove a smoothness condition for these renormalised diagrams. The renormalisation of diagrams without tadpoles is treated from the perspective of causal perturbation theory. A locally covariant construction of renormalisation maps is given for Feynman diagrams with edges labelled by conormal distributions.
Keywords: Microlocal Analysis; Quantum Field Theory; Feynman Diagrams; Perturbative Algebraic Quantum Field Theory; Wick Polynomials; Tadpole Renormalization; Lagrangian Distributions; Conormal Distributions; Epstein-Glaser Renormalization; Wavefront Sets; Functional formalism; Fourier Integral Operators; Pseudodifferential Operators; Singular Traces; Deformation Quantization; Renormalization Maps; Causal Perturbation Theory
 
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