Racah algebra
E443146
Racah algebra is a mathematical structure in representation theory and quantum mechanics that encodes the symmetries and coupling properties of angular momenta, particularly through Racah coefficients and related special functions.
Observed surface forms (1)
| Surface form | Occurrences |
|---|---|
| Wigner 6-j symbols | 1 |
Statements (43)
| Predicate | Object |
|---|---|
| instanceOf |
algebra
ⓘ
mathematical structure ⓘ noncommutative algebra ⓘ |
| appearsIn |
representation theory of rotation group SO(3)
ⓘ
representation theory of su(2) ⓘ |
| connectedTo |
Clebsch–Gordan coefficients
NERFINISHED
ⓘ
Lie algebra representations ⓘ Wigner 3-j symbols NERFINISHED ⓘ Wigner 9-j symbols NERFINISHED ⓘ quantum group symmetries ⓘ |
| encodes |
coupling properties of angular momenta
ⓘ
symmetries of angular momentum coupling ⓘ |
| field |
mathematical physics
ⓘ
mathematics ⓘ quantum mechanics ⓘ representation theory ⓘ |
| frameworkFor |
algebraic treatment of 6-j symbols
ⓘ
recoupling theory ⓘ |
| generalizationOf | angular momentum coupling algebra ⓘ |
| governs | recoupling transformations of angular momenta ⓘ |
| hasApplication |
calculation of coupling coefficients
ⓘ
calculation of transition amplitudes ⓘ spectral analysis of quantum systems ⓘ |
| hasProperty |
associative
ⓘ
noncommutative ⓘ |
| hasRole |
algebraic framework for Racah coefficients
ⓘ
symmetry algebra of certain special functions ⓘ |
| namedAfter | Giulio Racah NERFINISHED ⓘ |
| relatedTo |
Racah coefficients
ⓘ
Racah polynomials NERFINISHED ⓘ Wigner 6-j symbols NERFINISHED ⓘ orthogonal polynomials ⓘ special functions ⓘ |
| studiedIn |
algebraic methods in quantum mechanics
ⓘ
theory of exactly solvable models ⓘ |
| symmetryOf |
Racah polynomials
NERFINISHED
ⓘ
certain hypergeometric-type difference equations ⓘ |
| usedIn |
addition of angular momenta
ⓘ
atomic physics ⓘ molecular physics ⓘ nuclear physics ⓘ quantum angular momentum theory ⓘ spectroscopic coupling schemes ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Wigner 6-j symbols