John Gough, Joachim KupschCambridge University Press, 4/12/2018EAN 9781108416764, ISBN10: 1108416764Hardcover, 338 pages, 23.4 x 15.5 x 2.4 cmLanguage: EnglishWick 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.PrefaceNotation1. Introduction to combinatorics2. Probabilistic Moments and Cumulants3. Quantum probability4. Quantum fields5. Combinatorial species6. Combinatorial aspects of quantum fieldsFeynman diagrams7. Entropy, large deviations and legendre transforms8. Introduction to Fock spaces9. Operators and fields on the Boson Fock space10. L2-representations of the Boson Fock space11. Local fields on the Boson Fock spacefree fields12. Local fields on the Boson Fock spaceinteracting fields13. Quantum stochastic calculus14. Quantum stochastic limitsBibliographyIndex.
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