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Quantum Field Theory for Mathematicians

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: April 2008
  • availability: Available
  • format: Paperback
  • isbn: 9780521060257

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  • The approach to quantum field theory in this book is part way between building a mathematical model of the subject and presenting the mathematics that physicists actually use. It starts with the need to combine special relativity and quantum mechanics and culminates in a basic understanding of the standard model of electroweak and strong interactions. The book is divided into five parts: 1. Canonical quantization of scalar fields; 2. Weyl, Dirac and vector fields; 3. Functional integral quantization; 4. The standard model of the electroweak and strong interactions; 5. Renormalization. This should be a useful reference for anybody with interests in quantum theory and related areas of function theory, functional analysis, differential geometry or topological invariant theory.

    • Gives a unique mathematical development of the subject
    • Based on courses given at Harvard
    • Includes many exercises and solutions
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    Product details

    • Date Published: April 2008
    • format: Paperback
    • isbn: 9780521060257
    • length: 716 pages
    • dimensions: 235 x 155 x 35 mm
    • weight: 0.997kg
    • availability: Available
  • Table of Contents

    1. Relativistic quantum mechanics
    2. Fock space, the scalar field and canonical quantization
    3. Symmetries, conserved currents and conserved quantities
    4. The scattering matrix and Feynmann diagrams
    5. Differential transition probabilities and predictions
    6. Representations of the Lorentz group
    7. Two-component scalar fields
    8. Four-component scalar fields
    9. Massive vector fields
    10. Reformulating scattering theory
    11. Functional integral quantization
    12. Quantization of gauge theories
    13. Anomalies of gauge theories
    14. SU(3) representation theory
    15. The structure of the standard model
    16. Hadrons, flavor symmetry and nucleon-pion interactions
    17. Tree-level applications of the standard model
    18. Regularization and renormalization
    19. Renormalization of QED
    20. Renormalization and preservation of symmetries
    21. The renormalization group equations.

  • Author

    Robin Ticciati, Maharishi University of Management, Iowa

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