Combinatorics and physics
Combinatorial physics or physical combinatorics is the area of interaction between physics and combinatorics.Overview
Combinatorics has always played an important role in quantum field theory and statistical physics. However, combinatorial physics only emerged as a specific field after a seminal work by Alain Connes and Dirk Kreimer, showing that the renormalization of Feynman diagrams can be described by a Hopf algebra.
Combinatorial physics can be characterized by the use of algebraic concepts to interpret and solve physical problems involving combinatorics. It gives rise to a particularly harmonious collaboration between mathematicians and physicists.
Among the significant physical results of combinatorial physics, we may mention the reinterpretation of renormalization as a Riemann–Hilbert problem, the fact that the Slavnov–Taylor identities of gauge theories generate a Hopf ideal, the quantization of fields and strings, and a completely algebraic description of the combinatorics of quantum field theory. The important example of editing combinatorics and physics is relation between enumeration of alternating sign matrix and ice-type model. Corresponding ice-type model is six vertex model with domain wall boundary conditions.Combinatorics and statistical physics
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- , Graham Brightwell, Peter Winkler
- , Jaroslav Nešetřil, Peter Winkler, AMS Bookstore, 2001,
Conference proceedings
- Proc. of Combinatorics and Physics, Los Alamos, August 1998
- , Anatol N. Kirillov, Akihiro Tsuchiya, Hiroshi Umemura, World Scientific, 2001,
- , Anatol N. Kirillov, Nadejda Liskova, World Scientific, 2001,
- , Anatoliĭ, Moiseevich Vershik, Springer, 2002,
- , 10–15 July 2005, Dunk Island, Queensland, Australia
- Proceedings of the Conference on Combinatorics and Physics, MPIM Bonn, March 19–23, 2007
