Combinatorics and physics
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Combinatorial physics or physical combinatorics is the area of interaction between physics and combinatorics.
Overview
Summarize
Perspective
- "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–Hilbert problem,[5] the fact that the Slavnov–Taylor 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] An important example of applying combinatorics to physics is the enumeration of alternating sign matrix in the solution of ice-type models. The corresponding ice-type model is the six vertex model with domain wall boundary conditions.
See also
References
Further reading
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