Mathematical Aspects of Quantum Field Theory

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Cambridge University Press, Aug 12, 2010 - Science
Over the last century quantum field theory has made a significant impact on the formulation and solution of mathematical problems and inspired powerful advances in pure mathematics. However, most accounts are written by physicists, and mathematicians struggle to find clear definitions and statements of the concepts involved. This graduate-level introduction presents the basic ideas and tools from quantum field theory to a mathematical audience. Topics include classical and quantum mechanics, classical field theory, quantization of classical fields, perturbative quantum field theory, renormalization, and the standard model. The material is also accessible to physicists seeking a better understanding of the mathematical background, providing the necessary tools from differential geometry on such topics as connections and gauge fields, vector and spinor bundles, symmetries and group representations.
 

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Contents

1 Classical mechanics
1
2 Quantum mechanics
14
3 Relativity the Lorentz group and Diracs equation
51
4 Fiber bundles connections and representations
65
5 Classical field theory
93
6 Quantization of classical fields
117
7 Perturbative quantum field theory
153
8 Renormalization
192
9 The Standard Model
204
Hilbert spaces and operators
232
C algebras and spectral theory
258
Bibliography
289
Index
293
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About the author (2010)

Edson de Faria is a Professor in the Instituto de Matemática e Estatística at the Universidade de São Paulo.

Welington de Melo is a Professor in the Instituto de Matemática Pura e Aplicada in Rio de Janeiro.