Mathematics of Quantization and Quantum Fields
eBook - PDF

Mathematics of Quantization and Quantum Fields

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Mathematics of Quantization and Quantum Fields

About this book

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.

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Yes, you can access Mathematics of Quantization and Quantum Fields by Christian Gérard,Jan Dereziński in PDF and/or ePUB format, as well as other popular books in Physical Sciences & Mathematical & Computational Physics. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Contents
  2. Introduction
  3. 1 Vector spaces
  4. 2 Operators in Hilbert spaces
  5. 3 Tensor algebras
  6. 4 Analysis in L2(Rd)
  7. 5 Measures
  8. 6 Algebras
  9. 7 Anti-symmetric calculus
  10. 8 Canonical commutation relations
  11. 9 CCR on Fock space
  12. 10 Symplectic invariance of CCR in finite-dimensions
  13. 11 Symplectic invariance of the CCR on Fock spaces
  14. 12 Canonical anti-commutation relations
  15. 13 CAR on Fock spaces
  16. 14 Orthogonal invariance of CAR algebras
  17. 15 Clifford relations
  18. 16 Orthogonal invariance of the CAR on Fock spaces
  19. 17 Quasi-free states
  20. 18 Dynamics of quantum fields
  21. 19 Quantum fields on space-time
  22. 20 Diagrammatics
  23. 21 Euclidean approach for bosons
  24. 22 Interacting bosonic fields
  25. References
  26. Symbols index
  27. Subject index