From Classical Field Theory to Perturbative Quantum Field Theory

1. Front Matter

   Pages i-xxi

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2. Classical Field Theory

   • Michael Dütsch

   Pages 3-43

3. Deformation Quantization of the Free Theory

   • Michael Dütsch

   Pages 45-69

4. Perturbative Quantum Field Theory

   • Michael Dütsch

   Pages 71-298

5. Symmetries – the Master Ward Identity

   • Michael Dütsch

   Pages 299-348

6. Quantum Electrodynamics

   • Michael Dütsch

   Pages 349-461

7. Back Matter

   Pages 463-538

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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.

• deformation quantization
• classical field theory
• symmetries
• quantum electrodynamics
• renormalization group
• wave front set
• partial differential equations

“This book is a wonderful piece of scholarship, aimed at an audience of serious and correspondingly well-prepared mathematical physicists, or even mathematicians interested in this marvelous material and willing to play the long game.” (Michael Berg, MAA Reviews, September 15, 2019)

• University of Göttingen, Göttingen, Germany

  Michael Dütsch

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