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Quantum Fields and Processes: A Combinatorial Approach by John Gough

Quantum Fields and Processes: A Combinatorial Approach

by John Gough , Joachim Kupsch
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Book cover type: Hardcover
  • ISBN13: 9781108416764
  • Binding: Hardcover
  • Subject: N/A
  • Publisher: Cambridge University Press
  • Publisher Imprint: Cambridge University Press
  • Publication Date: N/A
  • Pages: 338
  • Original Price: GBP 73.0
  • Language: English
  • Edition: N/A
  • Item Weight: 604 grams
  • BISAC Subject(s): Probability & Statistics / General

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.

Gough, John: - 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.

Kupsch, Joachim: - 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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