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The 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.
List of contents
- 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
About the author
Between 2010 and 2015, Adrian Tanasa was an Associate Professor at Paris North University. In September 2015, he became a Full Professor at Bordeaux University. He is the founder of the journal "Annals of the Institut Henri Poincaré D, Combinatorics, Physics and their Interactions".
Summary
The 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.
