Combinatorial Physics
Combinatorics, Quantum Field Theory, and Quantum Gravity Models
Published on 16. April 2021
Book
Hardback
410 pages
978-0-19-289549-3 (ISBN)
Description
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.
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.
Reviews / Votes
A 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 *More details
Edition
1
Language
English
Place of publication
Oxford
United Kingdom
Target group
Professional and scholarly
Product notice
sewn/stitched
Cloth over boards
Illustrations
Graphs and line drawings
Dimensions
Height: 248 mm
Width: 173 mm
Thickness: 25 mm
Weight
944 gr
ISBN-13
978-0-19-289549-3 (9780192895493)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
E-Book
04/2021
1st Edition
OUP eBook
€98.99
Available for download
Person
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 Poincare D, Combinatorics, Physics and their Interactions".
Content
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
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