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    • Publisher:
      Cambridge University Press
      Publication date:
      November 2022
      February 2023
      ISBN:
      9781009290876
      9781009290821
      9781009290838
      Creative Commons:
      Creative Common License - CC Creative Common License - BY Creative Common License - NC Creative Common License - ND
      This content is Open Access and distributed under the terms of the Creative Commons Attribution licence CC-BY-NC-ND 4.0.
      https://creativecommons.org/creativelicenses
      Dimensions:
      (244 x 170 mm)
      Weight & Pages:
      1.34kg, 688 Pages
      Dimensions:
      (244 x 170 mm)
      Weight & Pages:
      1.18kg, 688 Pages
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    Book description

    Unifying topics that are scattered throughout the literature, this book offers a definitive review of mathematical aspects of quantization and quantum field theory. It presents both basic and advanced topics of quantum field theory in a mathematically consistent way, focusing on canonical commutation and anti-commutation relations. It begins with a discussion of the mathematical structures underlying free bosonic or fermionic fields: tensors, algebras, Fock spaces, and CCR and CAR representations. 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 mathematics and physics. This title, first published in 2013, has been reissued as an Open Access publication on Cambridge Core.

    Reviews

    '… offers much highly valuable material.'

    Stig Stenholm Source: Contemporary Physics

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    Contents

    Full book PDF
    • Frontmatter
      pp i-vi
    • Dedication
      pp vii-viii
    • Contents
      pp ix-xii
    • Introduction
      pp 1-7
    • 1 - Vector spaces
      pp 8-35
    • 2 - Operators in Hilbert spaces
      pp 36-56
    • 3 - Tensor algebras
      pp 57-91
    • 4 - Analysis in L2(Rd)
      pp 92-110
    • 5 - Measures
      pp 111-141
    • 6 - Algebras
      pp 142-158
    • 7 - Anti–symmetric calculus
      pp 159-172
    • 8 - Periodic magnetic channels
      pp 173-211
    • 9 - CCR on Fock space
      pp 212-238
    • 10 - Symplectic invariance of CCR in finite–dimensions
      pp 239-265
    • 11 - Symplectic invariance of the CCR on Fock spaces
      pp 266-312
    • 12 - Canonical anti–commutation relations
      pp 313-336
    • 13 - CAR on Fock spaces
      pp 337-350
    • 14 - Orthogonal invariance of CAR algebras
      pp 351-367
    • 15 - Clifford relations
      pp 368-385
    • 16 - Orthogonal invariance of the CAR on Fock spaces
      pp 386-422
    • 17 - Quasi–free states
      pp 423-474
    • 18 - Dynamics of quantum fields
      pp 475-511
    • 19 - Quantum fields on space–time
      pp 512-554
    • 20 - Diagrammatics
      pp 555-604
    • 21 - Euclidean approach for bosons
      pp 606-640
    • 22 - Interacting bosonic fields
      pp 641-660
    • References
      pp 661-667
    • Symbols index
      pp 668-670
    • Subject index
      pp 671-676

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