Ist product table.m

Structure coefficient tables for the associative envelopes of su(mult) algebras.

Syntax

    [product_table_left,product_table_right]=ist_product_table(mult)

Arguments

    mult      - multiplicity, the number of energy levels
                of the spin in question

Outputs

Output contains the structure coefficients in the following conventions:

 product_table_left(n,m,k)=trace(T{n}*T{m}*T{k}')/...
                           sqrt(trace(T{k}*T{k}')*trace(T{m}*T{m}'))

 product_table_right(n,m,k)=trace(T{m}*T{n}*T{k}')/...
                            sqrt(trace(T{k}*T{k}')*trace(T{m}*T{m}')));

corresponding to the IST expansion of the left and right multiplicative action by T{n} on T{m}, as given in Eq 7.18 of the first edition of IK's book (normalisation is missing in the book, that's a typo). Numbering translation between single and double index is given by lm2lin.m and lin2lm.m.

Notes

These are expensive tables: disk cache is created and used automatically. The smallest and most frequently used case is hard-coded.

See also

irr_sph_ten.m, pauli.m

SU(2), SO(3), and other groups

Version 2.8, authors: Ilya Kuprov