Combinatorial physics or physical combinatorics is the area of interaction between
physics and
combinatorics.
Overview
"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]
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.
Combinatorial physics or physical combinatorics is the area of interaction between
physics and
combinatorics.
Overview
"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]
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.