Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
LieART: Lie Algebras and Representation Theory
The primary purpose of LieART is the tensor product and subalgebra decomposition of irreducible representations (irreps) of Lie algebras. These tasks are frequently needed in particle physics, where multiparticle fields are assigned to irreps. Tensor products of irreps are thus commonly used to find singlets suitable for the Lagrangian. Spontaneous symmetry breaking corresponds to the subalgebra decomposition.
For an introduction to the most important functions and common tasks see the Quick Start Tutorial.
Algebras
Roots
— Complete root system of an algebra
— Only the positive roots of an algebra
— Simple roots of an algebra in orthogonal coordinates
Weights
— Complete weight system of a representation
Representations
— Irreducible representation
— Compute the dimension of a representation
— Displays the Young tableau corresponding to an SU(N) representation
Decompositions
— Decompose tensor products of irreps
— Decompose irrep to subalgebras
Displaying Output
— Textbook style sum of a list irreps
 |
|
|
""