Quantum Fields and Processes

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 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.

• 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.

'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