Mathematical Aspects of Quantum Field Theory

Nonfiction, Science & Nature, Science, Physics, Mathematical Physics, Mathematics
Cover of the book Mathematical Aspects of Quantum Field Theory by Edson de Faria, Welington de Melo, Cambridge University Press
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Author: Edson de Faria, Welington de Melo ISBN: 9781139635523
Publisher: Cambridge University Press Publication: August 12, 2010
Imprint: Cambridge University Press Language: English
Author: Edson de Faria, Welington de Melo
ISBN: 9781139635523
Publisher: Cambridge University Press
Publication: August 12, 2010
Imprint: Cambridge University Press
Language: English

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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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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