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Mathematics of Quantization and Quantum Fields

$170.00 (C)

Part of Cambridge Monographs on Mathematical Physics

  • Date Published: April 2013
  • availability: Available
  • format: Hardback
  • isbn: 9781107011113

$ 170.00 (C)

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About the Authors
  • Unifying a range of topics that are currently scattered throughout the literature, this book offers a unique and definitive review of mathematical aspects of quantization and quantum field theory. The authors present both basic and more advanced topics of quantum field theory in a mathematically consistent way, focusing on canonical commutation and anti-commutation relations. They begin with a discussion of the mathematical structures underlying free bosonic or fermionic fields, like tensors, algebras, Fock spaces, and CCR and CAR representations (including their symplectic and orthogonal invariance). Applications of these topics to physical problems are discussed in later chapters. Although most of the book is devoted to free quantum fields, it also contains an exposition of two important aspects of interacting fields: diagrammatics and the Euclidean approach to constructive quantum field theory. With its in-depth coverage, this text is essential reading for graduate students and researchers in departments of mathematics and physics.

    • Unifies various aspects of quantization and quantum fields, encouraging a deeper understanding of some of the mathematical aspects of quantum field theory
    • Fills a gap in the market by focusing on the mathematical aspects of quantum field theory
    • Depth of coverage - the reader will find rigorous mathematical results
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    "… offers much highly valuable material."
    Stig Stenholm, Contemporary Physics

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    Product details

    • Date Published: April 2013
    • format: Hardback
    • isbn: 9781107011113
    • length: 688 pages
    • dimensions: 244 x 170 x 37 mm
    • weight: 1.29kg
    • contains: 11 b/w illus. 5 tables
    • availability: Available
  • Table of Contents

    1. Vector spaces
    2. Operators in Hilbert spaces
    3. Tensor algebras
    4. Analysis in L2(Rd)
    5. Measures
    6. Algebras
    7. Anti-symmetric calculus
    8. Canonical commutation relations
    9. CCR on Fock spaces
    10. Symplectic invariance of CCR in finite dimensions
    11. Symplectic invariance of the CCR on Fock spaces
    12. Canonical anti-commutation relations
    13. CAR on Fock spaces
    14. Orthogonal invariance of CAR algebras
    15. Clifford relations
    16. Orthogonal invariance of the CAR on Fock spaces
    17. Quasi-free states
    18. Dynamics of quantum fields
    19. Quantum fields on space-time
    20. Diagrammatics
    21. Euclidean approach for bosons
    22. Interacting bosonic fields
    Subject index
    Symbols index.

  • Authors

    Jan Dereziński, Uniwersytet Warszawski, Poland
    Jan Dereziński is a Professor in the Faculty of Physics at the University of Warsaw. His research interests cover various aspects of quantum physics and quantum field theory, especially from the rigorous point of view.

    Christian Gérard, Université Paris-Sud
    Christian Gérard is a Professor in the Département de Mathématiques at the Université Paris-Sud. He was previously Directeur de Recherche at the CNRS (Centre National de la Recherche Scientifique). His research interests are the spectral and scattering theory in non-relativistic quantum mechanics and in quantum field theory.

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