Combinatorial Physics

Combinatorics, Quantum Field Theory, and Quantum Gravity Models
1. Auflage 2021
ISBN: 978-0-19-289549-3
Verlag: Oxford University Press

Buch, Englisch, 410 Seiten, Format (B × H): 173 mm x 248 mm, Gewicht: 944 g

The interplay between combinatorics and theoretical physics is a recent trend which appears to us as particularly natural, since the unfolding of new ideas in physics is often tied to the development of combinatorial methods, and, conversely, problems in combinatorics have been successfully tackled using methods inspired by theoretical physics. We can thus speak nowadays of an emerging domain of Combinatorial Physics.

The interference between these two disciplines is moreover an interference of multiple facets. Its best known manifestation (both to combinatorialists and theoretical physicists) has so far been the one between combinatorics and statistical physics, as statistical physics relies on an accurate counting of the various states or configurations of a physical system.

But combinatorics and theoretical physics interact in various other ways. This book is mainly dedicated to the interactions of combinatorics (algebraic, enumerative, analytic) with (commutative and non-commutative) quantum field theory and tensor models, the latter being seen as a quantum field theoretical generalisation of matrix models.

Autoren/Hrsg.

Tanasa, Adrian

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik EDV | Informatik Informatik

Inhaltsverzeichnis

- 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

Über Autor(innen)

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".