Dimensional Regularization in Position Space and a Forest Formula for Regularized Epstein-Glaser Renormalization

Abstract

The present work contains a consistent formulation of the methods of dimensional regularization (DimReg) and minimal subtraction (MS) in Minkowski position space. The methods are implemented into the framework of perturbative Algebraic Quantum Field Theory (pAQFT). The developed methods are used to solve the Epstein-Glaser recursion for the construction of time-ordered products in all orders of causal perturbation theory. A solution is given in terms of a forest formula in the sense of Zimmermann. A relation to the alternative approach to renormalization theory using Hopf algebras is established.

PhD thesis, 107 pages, 3 figures

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Cited by in corpus (10)

• Construction of KMS States in Perturbative QFT and Renormalized Hamiltonian Dynamics
• Fermionic fields in the functional approach to classical field theory
• Dimensional Regularization in Position Space, and a Forest Formula for Epstein-Glaser Renormalization
• Complex powers of analytic functions and meromorphic renormalization in QFT
• Improved Epstein-Glaser renormalization in $x$-space versus differential renormalization
• Correlators, Feynman diagrams, and quantum no-hair in deSitter spacetime
• Fully renormalized stress tensor correlator in flat space
• Perturbative BF theory
• Normal Products and Zimmermann Identities in Configuration Space BPHZ Renormalization
• Remarks on local symmetry invariance in perturbative algebraic quantum field theory