Ebook: Perturbative Quantum Electrodynamics and Axiomatic Field Theory

This book demonstrates that fundamental concepts and methods from phenomenological particle physics can be derived rigorously from well-defined general assumptions in a mathematically clean way. Starting with the Wightman formulation of relativistic quantum field theory, the perturbative formulation of quantum electrodynamics is derived avoiding the usual formalism based on the canonical commutation relations. A scattering formalism based on the local-observables approach is developed, directly yielding expressions for the observable inclusive cross-sections without having to introduce the S-matrix. Neither ultraviolet nor infrared regularizations are required in this approach. Although primarily intended for researchers working in this field, anyone with a basic working knowledge of relativistic quantum field theory can benefit from this book.

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This book demonstrates that fundamental concepts and methods from phenomenological particle physics can be derived rigorously from well-defined general assumptions in a mathematically clean way. Starting with the Wightman formulation of relativistic quantum field theory, the perturbative formulation of quantum electrodynamics is derived avoiding the usual formalism based on the canonical commutation relations. A scattering formalism based on the local-observables approach is developed, directly yielding expressions for the observable inclusive cross-sections without having to introduce the S-matrix. Neither ultraviolet nor infrared regularizations are required in this approach. Although primarily intended for researchers working in this field, anyone with a basic working knowledge of relativistic quantum field theory can benefit from this book.

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This book demonstrates that fundamental concepts and methods from phenomenological particle physics can be derived rigorously from well-defined general assumptions in a mathematically clean way. Starting with the Wightman formulation of relativistic quantum field theory, the perturbative formulation of quantum electrodynamics is derived avoiding the usual formalism based on the canonical commutation relations. A scattering formalism based on the local-observables approach is developed, directly yielding expressions for the observable inclusive cross-sections without having to introduce the S-matrix. Neither ultraviolet nor infrared regularizations are required in this approach. Although primarily intended for researchers working in this field, anyone with a basic working knowledge of relativistic quantum field theory can benefit from this book.
Content:
Front Matter....Pages I-IX
Introduction....Pages 1-4
Front Matter....Pages 5-5
Relativistic Covariance....Pages 7-17
Electrodynamics as a Classical Field Theory....Pages 19-24
The Basic Principles of Relativistic Quantum Field Theory....Pages 25-37
Free Fields....Pages 39-66
An Outline of Interacting QED....Pages 67-83
The Electric Charges....Pages 85-91
Front Matter....Pages 93-93
The Program of Perturbation Theory....Pages 95-108
Unrenormalized Solution....Pages 109-134
Renormalization and the UV Problem....Pages 135-163
The IR Problem for Wightman Functions....Pages 165-186
Physical States....Pages 187-210
Front Matter....Pages 211-211
The Standard View....Pages 213-220
Particle Probes....Pages 221-237
Interacting Particles....Pages 239-281
Reactions....Pages 283-319
Cross Sections....Pages 321-345
Back Matter....Pages 347-357

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This book demonstrates that fundamental concepts and methods from phenomenological particle physics can be derived rigorously from well-defined general assumptions in a mathematically clean way. Starting with the Wightman formulation of relativistic quantum field theory, the perturbative formulation of quantum electrodynamics is derived avoiding the usual formalism based on the canonical commutation relations. A scattering formalism based on the local-observables approach is developed, directly yielding expressions for the observable inclusive cross-sections without having to introduce the S-matrix. Neither ultraviolet nor infrared regularizations are required in this approach. Although primarily intended for researchers working in this field, anyone with a basic working knowledge of relativistic quantum field theory can benefit from this book.
Content:
Front Matter....Pages I-IX
Introduction....Pages 1-4
Front Matter....Pages 5-5
Relativistic Covariance....Pages 7-17
Electrodynamics as a Classical Field Theory....Pages 19-24
The Basic Principles of Relativistic Quantum Field Theory....Pages 25-37
Free Fields....Pages 39-66
An Outline of Interacting QED....Pages 67-83
The Electric Charges....Pages 85-91
Front Matter....Pages 93-93
The Program of Perturbation Theory....Pages 95-108
Unrenormalized Solution....Pages 109-134
Renormalization and the UV Problem....Pages 135-163
The IR Problem for Wightman Functions....Pages 165-186
Physical States....Pages 187-210
Front Matter....Pages 211-211
The Standard View....Pages 213-220
Particle Probes....Pages 221-237
Interacting Particles....Pages 239-281
Reactions....Pages 283-319
Cross Sections....Pages 321-345
Back Matter....Pages 347-357
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