Overview

GroupFunctions.jl computes matrix elements of irreducible representations of the unitary group U(n), both numerically and symbolically. Given a unitary matrix and an irrep label, it returns the corresponding transformation matrix, with basis states represented by Gelfand-Tsetlin patterns.

julia> using GroupFunctions
julia> U = su2_block_symbolic(2,1);
julia> U2×2 Matrix{SymEngine.Basic}:
 v_1_1  v_1_2
 v_2_1  v_2_2
julia> group_function([2,0], U)[1]3×3 Matrix{SymEngine.Basic}:
             v_2_2^2        sqrt(2)*v_2_2*v_2_1              v_2_1^2
 sqrt(2)*v_1_2*v_2_2  v_1_1*v_2_2 + v_1_2*v_2_1  sqrt(2)*v_1_1*v_2_1
             v_1_2^2        sqrt(2)*v_1_1*v_1_2              v_1_1^2

This computes the SU(2) irreps for symbolic matrices.

Installation

If this is your first time using Julia, please refer to the language documentation and tutorials. Until the package is registered, please use the manual installation using git URL: open up julia, and within the interpreter perform the following:

julia> # here you need to press the character `]`; the prompt turns blue
pkg> add https://github.com/davidamaro/GroupFunctions.jl

Requires Julia ≥ 1.6.

Contact

Questions and suggestions: david.amaroalcala@savba.sk

References