[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/en\/wiki12\/combinatorics-and-physics-wikipedia\/#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/en\/wiki12\/combinatorics-and-physics-wikipedia\/","headline":"Combinatorics and physics – Wikipedia","name":"Combinatorics and physics – Wikipedia","description":"From Wikipedia, the free encyclopedia Combinatorial physics or physical combinatorics is the area of interaction between physics and combinatorics. Overview[edit]","datePublished":"2020-01-20","dateModified":"2020-01-20","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/en\/wiki12\/author\/lordneo\/#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/en\/wiki12\/author\/lordneo\/","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/en.wikipedia.org\/wiki\/Special:CentralAutoLogin\/start?type=1x1","url":"https:\/\/en.wikipedia.org\/wiki\/Special:CentralAutoLogin\/start?type=1x1","height":"1","width":"1"},"url":"https:\/\/wiki.edu.vn\/en\/wiki12\/combinatorics-and-physics-wikipedia\/","about":["Wiki"],"wordCount":2002,"articleBody":"From Wikipedia, the free encyclopediaCombinatorial physics or physical combinatorics is the area of interaction between physics and combinatorics.Overview[edit]“Combinatorial Physics is an emerging area which unites combinatorial and discrete mathematical techniques applied to theoretical physics, especially Quantum Theory.”[1]“Physical combinatorics might be defined naively as combinatorics guided by ideas or insights from physics”[2]Combinatorics has always played an important role in quantum field theory and statistical physics.[3] However, combinatorial physics only emerged as a specific field after a seminal work by Alain Connes and Dirk Kreimer,[4] 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\u2013Hilbert problem,[5] the fact that the Slavnov\u2013Taylor identities of gauge theories generate a Hopf ideal,[6] the quantization of fields[7] and strings,[8] and a completely algebraic description of the combinatorics of quantum field theory.[9] 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.See also[edit]References[edit]^ 2007 International Conference on Combinatorial physics^ Physical Combinatorics, Masaki Kashiwara, Tetsuji Miwa, Springer, 2000, ISBN\u00a00-8176-4175-0^ David Ruelle (1999). Statistical Mechanics, Rigorous Results. World Scientific. ISBN\u00a0978-981-02-3862-9.^ A. Connes, D. Kreimer,Renormalization in quantum field theory and the Riemann-Hilbert problem I, Commun. Math. Phys. 210 (2000), 249-273^ A. Connes, D. Kreimer,Renormalization in quantum field theory and the Riemann-Hilbert problem II, Commun. Math. Phys. 216 (2001), 215-241^ W. D. van Suijlekom, Renormalization of gauge fields: A Hopf algebra approach, Commun. Math. Phys. 276 (2007), 773-798^ C. Brouder, B. Fauser, A. Frabetti, R. Oeckl, Quantum field theory and Hopf algebra cohomology, J. Phys. A: Math. Gen. 37 (2004), 5895-5927^ T. Asakawa, M. Mori, S. Watamura, Hopf Algebra Symmetry and String Theory, Prog. Theor. Phys. 120 (2008), 659-689^ C. Brouder, Quantum field theory meets Hopf algebra, Mathematische Nachrichten 282 (2009), 1664-1690Further reading[edit]Some Open Problems in Combinatorial Physics, G. Duchamp, H. CheballahOne-parameter groups and combinatorial physics, G. Duchamp, K.A. Penson, A.I. Solomon, A.Horzela, P.BlasiakCombinatorial Physics, Normal Order and Model Feynman Graphs, A.I. Solomon, P. Blasiak, G. Duchamp, A. Horzela, K.A. PensonHopf Algebras in General and in Combinatorial Physics: a practical introduction, G. Duchamp, P. Blasiak, A. Horzela, K.A. Penson, A.I. SolomonDiscrete and Combinatorial PhysicsBit-String Physics: a Novel “Theory of Everything”, H. Pierre NoyesCombinatorial Physics, Ted Bastin, Clive W. Kilmister, World Scientific, 1995, ISBN\u00a0981-02-2212-2Physical Combinatorics and Quasiparticles, Giovanni Feverati, Paul A. Pearce, Nicholas S. WitteFitzgerald, Hannah. “Physical Combinatorics of Non-Unitary Minimal Models” (PDF). CiteSeerX\u00a010.1.1.46.4129. Retrieved 17 August 2014.Paths, Crystals and Fermionic Formulae, G.Hatayama, A.Kuniba, M.Okado, T.Takagi, Z.TsuboiOn powers of Stirling matrices, Istv\u00e1n Mez\u0151“On cluster expansions in graph theory and physics”, N BIGGS\u00a0\u2014 The Quarterly Journal of Mathematics, 1978 – Oxford Univ PressEnumeration Of Rational Curves Via Torus Actions, Maxim Kontsevich, 1995Non-commutative Calculus and Discrete Physics, Louis H. Kauffman, February 1, 2008Sequential cavity method for computing free energy and surface pressure, David Gamarnik, Dmitriy Katz, July 9, 2008Combinatorics and statistical physics[edit]“Graph Theory and Statistical Physics”, J.W. Essam, Discrete Mathematics, 1, 83-112 (1971).Combinatorics In Statistical PhysicsHard Constraints and the Bethe Lattice: Adventures at the Interface of Combinatorics and Statistical Physics, Graham Brightwell, Peter WinklerGraphs, Morphisms, and Statistical Physics: DIMACS Workshop Graphs, Morphisms and Statistical Physics, March 19-21, 2001, DIMACS Center, Jaroslav Ne\u0161et\u0159il, Peter Winkler, AMS Bookstore, 2001, ISBN\u00a00-8218-3551-3Conference proceedings[edit]Proc. of Combinatorics and Physics, Los Alamos, August 1998Physics and Combinatorics 1999: Proceedings of the Nagoya 1999 International Workshop, Anatol N. Kirillov, Akihiro Tsuchiya, Hiroshi Umemura, World Scientific, 2001, ISBN\u00a0981-02-4578-5Physics and combinatorics 2000: proceedings of the Nagoya 2000 International Workshop, Anatol N. Kirillov, Nadejda Liskova, World Scientific, 2001, ISBN\u00a0981-02-4642-0Asymptotic combinatorics with applications to mathematical physics: a European mathematical summer school held at the Euler Institute, St. Petersburg, Russia, July 9-20, 2001, Anatoli\u012d, Moiseevich Vershik, Springer, 2002, ISBN\u00a03-540-40312-4Counting Complexity: An International Workshop On Statistical Mechanics And Combinatorics, 10\u201315 July 2005, Dunk Island, Queensland, AustraliaProceedings of the Conference on Combinatorics and Physics, MPIM Bonn, March 19\u201323, 2007"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/en\/wiki12\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/en\/wiki12\/combinatorics-and-physics-wikipedia\/#breadcrumbitem","name":"Combinatorics and physics – Wikipedia"}}]}]