Quadruple correlation functions and their application in double polarization experiments and in few-body problems

We define real functions which form a complete, orthogonal and rotational invariant basis for all problems depending on four directions. Their usefulness is demonstrated for processes of the type $\text{a}\text{+}\text{b}\text{→}\text{c}\text{+}\text{d}\text{,}\text{a}\text{+}\text{b}\text{→}\text{c}\text{+}\text{d}\text{,}\text{a}\text{+}\text{b}\text{→}\text{c}{}_1\text{, +}\text{c}{}_2\text{+}\text{d}$. The special case of all four directions in one plane has many applications too, e.g. in two- and three-body problems.