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Quantum Fields and Processes
A Combinatorial Approach

$79.99 (P)

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: April 2018
  • availability: In stock
  • format: Hardback
  • isbn: 9781108416764

$ 79.99 (P)
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  • Wick ordering of creation and annihilation operators is of fundamental importance for computing averages and correlations in quantum field theory and, by extension, in the Hudson–Parthasarathy theory of quantum stochastic processes, quantum mechanics, stochastic processes, and probability. This book develops the unified combinatorial framework behind these examples, starting with the simplest mathematically, and working up to the Fock space setting for quantum fields. Emphasizing ideas from combinatorics such as the role of lattice of partitions for multiple stochastic integrals by Wallstrom–Rota and combinatorial species by Joyal, it presents insights coming from quantum probability. It also introduces a 'field calculus' which acts as a succinct alternative to standard Feynman diagrams and formulates quantum field theory (cumulant moments, Dyson–Schwinger equation, tree expansions, 1-particle irreducibility) in this language. Featuring many worked examples, the book is aimed at mathematical physicists, quantum field theorists, and probabilists, including graduate and advanced undergraduate students.

    • Introduces a new combinatorial calculus that provides an alternative to the usual Feynman diagram expansions
    • Provides detailed worked examples that demonstrate a broad range of applications
    • Offers a unified approach to combinatorial formulas for multiple stochastic integrals
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    Reviews & endorsements

    'This book offers an excellent account of the probabilistic aspects of quantum theory, focused on the interplay between quantum field theory and quantum stochastic calculus. The text is highly accessible thanks to the careful choice of topics and the systematic use of elegant combinatorial and algebraic methods. This makes the book suitable for graduate level teaching and self-study. I highly recommend it as a timely addition to the classical literature on quantum probability.' Madalin Guta, University of Nottingham

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    Product details

    • Date Published: April 2018
    • format: Hardback
    • isbn: 9781108416764
    • length: 338 pages
    • dimensions: 234 x 155 x 24 mm
    • weight: 0.62kg
    • availability: In stock
  • Table of Contents

    Preface
    Notation
    1. Introduction to combinatorics
    2. Probabilistic Moments and Cumulants
    3. Quantum probability
    4. Quantum fields
    5. Combinatorial species
    6. Combinatorial aspects of quantum fields: Feynman diagrams
    7. Entropy, large deviations and legendre transforms
    8. Introduction to Fock spaces
    9. Operators and fields on the Boson Fock space
    10. L2-representations of the Boson Fock space
    11. Local fields on the Boson Fock space: free fields
    12. Local fields on the Boson Fock space: interacting fields
    13. Quantum stochastic calculus
    14. Quantum stochastic limits
    Bibliography
    Index.

  • Authors

    John Gough, Aberystwyth University
    John Gough is Professor of mathematical and theoretical physics at Aberystwyth University, Wales. He works in the field of quantum probability and open systems, especially quantum Markovian models that can be described in terms of the Hudson–Parthasarathy quantum stochastic calculus. His more recent work has been on the general theory of networks of quantum Markovian input-output and their applications to quantum feedback control.

    Joachim Kupsch, Technische Universität Kaiserslautern, Germany
    Joachim Kupsch is Professor Emeritus of theoretical physics at the Technische Universität Kaiserslautern, Germany. His research has focused on scattering theory, relativistic S-matrix theory, and infinite-dimensional analysis applied to quantum field theory. His publications have examined canonical transformations, fermionic integration, and superanalysis. His later work looks at open systems and decoherence and he coauthored a book on the subject in 2003.

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