Combinatorial Physics Combinatorics, Quantum Field Theory, and Quantum Gravity Models

by Tanasa, Adrian

• ISBN13: 9780192895493
• ISBN10: 0192895494
• Format: Hardcover
• Copyright: 2021-06-16
• Publisher: Oxford University Press

Author Biography

Adrian Tanasa, Full Professor, University of Bordeaux, France

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 Poincar? D, Combinatorics, Physics and their Interactions".

Table 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