Difference between revisions of "Ist product table.m"
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==Arguments== | ==Arguments== | ||
| − | mult - multiplicity of the spin in question | + | mult - multiplicity, the number of energy levels |
| + | of the spin in question | ||
==Outputs== | ==Outputs== | ||
| Line 17: | Line 18: | ||
product_table_right(n,m,k)=trace(T{m}*T{n}*T{k}')/... | product_table_right(n,m,k)=trace(T{m}*T{n}*T{k}')/... | ||
| − | sqrt(trace(T{k}*T{k}')*trace(T{m}*T{m}')); | + | sqrt(trace(T{k}*T{k}')*trace(T{m}*T{m}'))); |
| − | corresponding to Eq 7.18 of the first edition of IK's book (normalisation is missing in the book, that's a typo). | + | 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== | ==Notes== | ||
| − | These are expensive tables: disk cache is created and used automatically. | + | These are expensive tables: disk cache is created and used automatically. The smallest and most frequently used case is hard-coded. |
==See also== | ==See also== | ||
Revision as of 15:42, 5 June 2026
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
SU(2), SO(3), and other groups
Version 2.8, authors: Ilya Kuprov
