the coupling is the one for spherical tensors, with coefficients given by Clebsch-Gordan coefficients.
For instance (again considering A end B as tensor of rank 1)
\left[AB\right]_0=<1 0 1 0|1 0> A_0 B_0 +<1 -1 1 1|1 0> A_{-1} B_1 +<1 1 1 -1|1 0> A_{1} B_{-1} ,
where the Clebsch are <j1 m1 j2...
thanks He,
but still my problem remains, how to write down explicitly the term
you denote as 6AABB, taking into account that the tensors have a law
of composition or coupling. Is it correct to write AABB as the sum of all the possible
coupling of the four tensors to a scalar as I did in...
We know that the Newton binomial formula is valid for numbers
in elementary algebra.
Is there an equivalent formula for commuting spherical tensors? If so,
how is it?
To be specific let us suppose that A and B are two spherical tensors
of rank 1 and I want to calculate (A + B)4 and I want...