Skip to content

All SAP systems will be unavailable on Saturday 10th December 2022 from 0800-1800 UK Time.

If you can’t place an order, please contact Customer Services to complete your order.

UK/ROW +44 (0) 1223 326050 | US 1 800 872 7423 or 1 212 337 5000 | Australia/New Zealand 61 3 86711400 or 1800 005 210, New Zealand 0800 023 520

Register Sign in Wishlist

Quantum Fields and Processes
A Combinatorial Approach

$83.99 (C)

Part of Cambridge Studies in Advanced Mathematics

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

$ 83.99 (C)

Add to cart Add to wishlist

Other available formats:

Looking for an examination copy?

This title is not currently available for examination. However, if you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact providing details of the course you are teaching.

Product filter button
About the Authors
  • 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
    Read more

    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

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    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

    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

  • 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.

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.