Perturbative Quantum Electrodynamics and Axiomatic Field Theory

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Springer Science & Business Media, 17 apr 2013 - 355 pagine
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This book is concerned with relativistic quantum field theory, especially QED, its most successful example. It is set in the no-man's land between the math ematically rigorous but numerically barren general field theory of the math ematical physicist and the computationally fertile but mathematically some times adventurous field theory of the more phenomenologically inclined, and it aims at demonstrating that closer contact between these two disparate cultures may be of benefit to both. Perturbative QED serves as an exam ple. It is shown how the rules of perturbative quantum field theory, one of the major tools of phenomenology, can be derived from well-defined general assumptions in a mathematically clean way, in particular, not using any reg ularizations. Special emphasis is placed on giving the infrared problem its full due. This leads, among other things, to an unorthodox method based on the local-observables approach to field theory, of describing particles and their reactions. The resulting scattering formalism is immediately applica ble to the infraparticle situation of QED by directly yielding expressions for the observable-inclusive cross sections, dispensing with the notion of an S matrix. Interestingly enough, these expressions differ somewhat from those of the conventional approach. This point will hopefully give rise to interesting and fruitful discussions. I have been working on these sorts of problems on and off for a long time.

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Perturbation Theory
Electrodynamics as a Classical Field Theory 19
The Basic Principles of Relativistic Quantum Field Theory
Free Fields
An Outline of Interacting QED
The Electric Charges 85
The Program of Perturbation Theory 95
Unrenormalized Solution
The IR Problem for Wightman Functions
Physical States
Particles and Their Reactions
Particle Probes
Interacting Particles
Reactions 283
Cross Sections
References 347

Renormalization and the UV Problem

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