Description
Book SynopsisThe goal of the book is to use combinatorial techniques to solve fundamental physics problems, and vice-versa, to use theoretical physics techniques to solve combinatorial problems.
Trade ReviewA useful compendium of relevant subjects and it give the information about useful references in the field. * Juan Carlos Vazquez, zb Math Open *
An outstanding book on a recent and very timely topic. * Vincent Rivasseau, University Paris-Sud XI, Orsay *
This book appears at a time where there is a crucial need for such a cross-fertilisation of combinatorics and theoretical physics. * Thomas Krajewski, Aix-Marseille University *
Table of Contents1: Introduction 2: Graphs, maps and polynomials 3: Quantum field theory (QFT) 4: Tree weights and renormalization in QFT 5: Combinatorial QFT and the Jacobian Conjecture 6: Fermionic QFT, Grassmann calculus and combinatorics 7: Analytic combinatorics and QFT 8: Algebraic combinatorics and QFT 9: QFT on the non-commutative Moyal space and combinatorics 10: Quantum gravity, Group Field Theory and combinatorics 11: From random matrices to random tensors 12: Random tensor models - the U(N)D-invariant model 13: Random tensor models - the multi-orientable (MO) model 14: Random tensor models - the O(N)3 invariant model 15: The Sachdev-Ye-Kitaev holographic model 16: SYK-like tensor models Appendix A: Examples of tree weights B: Renormalization of the Grosse-Wulkenhaar model, one-loop examples C: The B+ operator in Moyal QFT, two-loop examples D: Explicit examples of GFT tensor Feynman integral computations E: Coherent states of SU(2) F: Proof of the double scaling limit of the U(N)D??invariant tensor model G: Proof of Theorem 15.3.2 H: Proof of Theorem 16.1.1 J: Summary of results on the diagrammatics of the coloured SYK model and of the Gurau-Witten model Bibliography
