Quantum Field Theory: A Tourist Guide for Mathematicians

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American Mathematical Soc., Aug 26, 2008 - Mathematics - 325 pages
Quantum field theory has been a great success for physics, but it is difficult for mathematicians to learn because it is mathematically incomplete. Folland, who is a mathematician, has spent considerable time digesting the physical theory and sorting out the mathematical issues in it. Fortunately for mathematicians, Folland is a gifted expositor. The purpose of this book is to present the elements of quantum field theory, with the goal of understanding the behavior of elementary particles rather than building formal mathematical structures, in a form that will be comprehensible to mathematicians. Rigorous definitions and arguments are presented as far as they are available, but the text proceeds on a more informal level when necessary, with due care in identifying the difficulties. The book begins with a review of classical physics and quantum mechanics, then proceeds through the construction of free quantum fields to the perturbation-theoretic development of interacting field theory and renormalization theory, with emphasis on quantum electrodynamics. The final two chapters present the functional integral approach and the elements of gauge field theory, including the Salam-Weinberg model of electromagnetic and weak interactions.
 

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Contents

Prologue
1
Review of Prequantum Physics
13
Basic Quantum Mechanics
33
Relativistic Quantum Mechanics
65
Free Quantum Fields
97
Quantum Fields with Interactions
123
Renormalization
191
Functional Integrals
257
Gauge Field Theories
291
Bibliography
317
IndeX
323
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