Regularization in quantum field theory from the causal point of view

Abstract

The causal approach to perturbative quantum field theory is presented in detail, which goes back to a seminal work by Henri Epstein and Vladimir Jurko Glaser in 1973. Causal perturbation theory is a mathematically rigorous approach to renormalization theory, which makes it possible to put the theoretical setup of perturbative quantum field theory on a sound mathematical basis. Epstein and Glaser solved this problem for a special class of distributions, the time-ordered products, that fulfill a causality condition, which itself is a basic requirement in axiomatic quantum field theory. In their original work, Epstein and Glaser studied only theories involving scalar particles. In this review, the extension of the method to theories with higher spin, including gravity, is presented. Furthermore, specific examples are presented in order to highlight the technical differences between the causal method and other regularization methods, like, e.g. dimensional regularization.

75 pages, 8 figures, style file included, some comments and references added

References in corpus (15)

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• The Master Ward Identity
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• Finite calculation of divergent selfenergy diagrams
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• Perturbative Gravity in the Causal Approach
• Dispersive calculation of the massless multi-loop sunrise diagram

Cited by in corpus (5)

• Normalizability analysis of the generalized quantum electrodynamics from the causal point of view
• Snowmass White Paper: The Quest to Define QFT
• Spontaneous emission and atomic line shift in causal perturbation theory
• Coulomb solutions from improper pseudo-unitary free gauge field operator translations
• Quantization due to the time evolution, with applications to Quantum Yang-Mills theory, Quantum Gravity and Classical Statistical Field Theory