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.
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.
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".
Inhaltsangabe
* 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
* 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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