Quantum Fields and Processes: A Combinatorial Approach (Cambridge Studies In Advanced Mathematics )

Synopsis

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.

Copyright:

2018

Book Details

Book Quality:

Publisher Quality

ISBN-13:

9781108266048

Related ISBNs:

9781108416764, 9781108416764

Publisher:

Cambridge University Press

Date of Addition:

06/15/18

Copyrighted By:

John Gough, Joachim Kupsch

Adult content:

No

Language:

English

Has Image Descriptions:

No

Categories:

Science, Mathematics and Statistics

Submitted By:

Bookshare Staff

Usage Restrictions:

This is a copyrighted book.