Quantum Fields and Processes: A Combinatorial Approach (Cambridge Studies in Advanced Mathematics)
Cambridge University Press, 4/12/2018
EAN 9781108416764, ISBN10: 1108416764
Hardcover, 338 pages, 23.4 x 15.5 x 2.4 cm
Language: English
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.
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.