Do quantum field theory without Feynman diagrams! Use the combinatorics behind cumulants, correlations, Green's functions and quantum fields.

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.

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.