The Action Principle in Epstein Glaser Renormalization and Renormalization of the S-Matrix in ${\varphi }^4$-Theory

Abstract

A formula describing finite renormalizations is derived in the Epstein-Glaser formalism and an explicit calculation of finite counterterms in ${\Phi }^4$-theory is performed. The Zimmermann identities and the action principle for changes of parameters in the interaction are presented independent of the adiabatic limit.

32 pages, added reference, corrected typos and changed content

References in corpus (3)

• Microlocal Analysis and Interacting Quantum Field Theories: Renormalization on Physical Backgrounds
• Lorentz Covariance in Epstein-Glaser Renormalization
• Gauge theories in local causal perturbation theory

Cited by in corpus (12)

• Causal perturbation theory in terms of retarded products, and a proof of the Action Ward Identity
• The Master Ward Identity and Generalized Schwinger-Dyson Equation in Classical Field Theory
• Renormalization as a functor on bialgebras
• The Master Ward Identity
• A Treatise on Quantum Clifford Algebras
• Dimensional Regularization in Position Space, and a Forest Formula for Epstein-Glaser Renormalization
• Dimensional Regularization in Position Space and a Forest Formula for Regularized Epstein-Glaser Renormalization
• UV and IR behaviour in QFT and LCQFT with fields as Operator Valued Distributions:Epstein and Glaser revisited
• Infrared problem in perturbative quantum field theory
• Spontaneous emission and atomic line shift in causal perturbation theory
• Local operators in the Sine-Gordon model: ${\partial }_{\mu }\varphi {\partial }_{\nu }\varphi$ and the stress tensor
• A quantum field algebra