ABSTRACT
An irreducible tensor is a tensor whose components transform linearly among themselves under rotations such that, if the whole rotation group is considered, all components of the tensor enter the linear combination (which does not exclude that for a certain rotation some coefficients in the linear combination vanish). Cartesian tensors of any rank can be generated by taking the direct product of two or more such tensors of lower rank. These tensors are not, however, irreducible with respect to rotations, because they contain parts which transform with a lower rank. Hence it is possible to construct tensors of any rank by composition—just as in the case of Cartesian tensors, although in a little more complicated way, but the great advantage is that the tensors so constructed are automatically irreducible if they are combined from two irreducible ones. Thus this kind of tensor is especially suited for all problems in which rotations come up.
