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Mathematical Aspects of Quantum Field Theory


Part of Cambridge Studies in Advanced Mathematics

Dennis Sullivan
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  • Date Published: August 2010
  • availability: Available
  • format: Hardback
  • isbn: 9780521115773

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About the Authors
  • 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.

    • Quantum field theory finally made accessible to mathematicians
    • A useful introduction for researchers in mathematics and mathematical physics
    • Provides both the mathematical tools and the necessary physical background, giving a more complete picture of the subjects
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    Reviews & endorsements

    '… a brief, but careful, reasonably balanced, and representative introduction for mathematicians to QFT as it is used in physics.' The Mathematical Intelligencer

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    Product details

    • Date Published: August 2010
    • format: Hardback
    • isbn: 9780521115773
    • length: 314 pages
    • dimensions: 235 x 158 x 20 mm
    • weight: 0.56kg
    • contains: 10 b/w illus. 45 exercises
    • availability: Available
  • Table of Contents

    Foreword Dennis Sullivan
    1. Classical mechanics
    2. Quantum mechanics
    3. Relativity, the Lorentz group and Dirac's equation
    4. Fiber bundles, connections and representations
    5. Classical field theory
    6. Quantization of classical fields
    7. Perturbative quantum field theory
    8. Renormalization
    9. The standard model
    Appendix A. Hilbert spaces and operators
    Appendix B. C* algebras and spectral theory

  • Authors

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

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


    Dennis Sullivan

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