Why the rank of an irreducible tensor must be an integer?

1. Nov 8, 2009

wdlang

why not half-integer?

according to the definition, such as [J_z,T^k_q]=q T^k_q

it is quite possible that k can be a half-integer.

2. Nov 9, 2009

DrDu

Well, in that context, a tensor has usually two indices, i.e. it transforms as the product of two equal irreducible representations of the rotation group these two representations may be either both integer or both half integer. In any case, the Clebsch Gordon decomposition will yield only integer representations.