YBE

E911205
abbreviation consistency condition integrability condition mathematical equation

YBE is an abbreviation for the Yang–Baxter equation, a fundamental consistency condition in mathematical physics and integrable systems that governs how particle-like excitations scatter and reorder.

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Observed surface forms (1)

Surface form Occurrences
Yang–Baxter equation 0

Statements (45)

Predicate Object
instanceOf abbreviation ⓘ
consistency condition ⓘ
integrability condition ⓘ
mathematical equation ⓘ
alsoKnownAs YBE NERFINISHED ⓘ
star–triangle relation ⓘ
centralConceptIn braid group representations ⓘ
theory of quantum groups ⓘ
describes consistency of three-body scattering ⓘ
factorization of multi-particle scattering ⓘ
reordering of particle-like excitations ⓘ
ensures associativity of scattering processes ⓘ
integrability of certain quantum models ⓘ
field integrable systems ⓘ
knot theory ⓘ
mathematical physics ⓘ
quantum field theory ⓘ
quantum groups ⓘ
statistical mechanics ⓘ
hasVariant classical Yang–Baxter equation NERFINISHED ⓘ
quantum Yang–Baxter equation NERFINISHED ⓘ
set-theoretic Yang–Baxter equation NERFINISHED ⓘ
implies commuting transfer matrices ⓘ
factorized S-matrix ⓘ
introducedInContextOf integrable models in statistical mechanics ⓘ
mathematicalDomain algebra ⓘ
category theory NERFINISHED ⓘ
low-dimensional topology ⓘ
representation theory ⓘ
namedAfter C. N. Yang NERFINISHED ⓘ
R. J. Baxter NERFINISHED ⓘ
refersTo Yang–Baxter equation NERFINISHED ⓘ
relatedTo Bethe ansatz NERFINISHED ⓘ
R-matrix NERFINISHED ⓘ
braid group NERFINISHED ⓘ
exactly solvable lattice models ⓘ
quantum inverse scattering method ⓘ
vertex models in statistical mechanics ⓘ
standsFor Yang–Baxter equation NERFINISHED ⓘ
type functional equation ⓘ
matrix equation ⓘ
usedIn construction of knot invariants ⓘ
construction of quantum groups ⓘ
integrable spin chains ⓘ
two-dimensional solvable models ⓘ

Referenced by (1)

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Yang–Baxter equation → alsoKnownAs → YBE ⓘ