图书简介

1 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

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