An international platform for information exchange among scientists working on
mathematical, conceptual, and constructive problems in
local relativistic quantum physics (LQP).

From Classical Field Theory to Perturbative Quantum Field Theory

Michael Dütsch
Progress in Mathematical Physics 74, Birkhäuser 2019
(2019)

This book develops a novel approach to perturbative quantum ﬁeld theory: starting with a perturbative formulation of classical ﬁeld theory, quantization is achieved by means of deformation quantization of the underlying free theory and by applying the principle that as much of the classical structure as possible should be maintained. The resulting formulation of perturbative quantum ﬁeld theory is a version of the Epstein-Glaser renormalization that is conceptually clear, mathematically rigorous and pragmatically useful for physicists. The connection to traditional formulations of perturbative quantum ﬁeld theory is also elaborated on, and the formalism is illustrated in a wealth of examples and exercises.

## Comments

## Abstract of the book

This book develops a novel approach to perturbative quantum ﬁeld theory: starting with a perturbative formulation of classical ﬁeld theory, quantization is achieved by means of deformation quantization of the underlying free theory and by applying the principle that as much of the classical structure as possible should be maintained. The resulting formulation of perturbative quantum ﬁeld theory is a version of the Epstein-Glaser renormalization that is conceptually clear, mathematically rigorous and pragmatically useful for physicists. The connection to traditional formulations of perturbative quantum ﬁeld theory is also elaborated on, and the formalism is illustrated in a wealth of examples and exercises.