Geometric measure of indistinguishability for groups of identical particles

The concept of p-orthogonality (1 <= p <= n) between n-particle states is introduced. It generalizes common orthogonality, which is equivalent to n-orthogonality, and strong orthogonality between fermionic states, which is equivalent to 1-orthogonality. Within the class of non-p-orthogonal states a finer measure of non-p-orthogonality is provided by Araki's angles between p-internal spaces. The p-orthogonality concept is a geometric measure of indistinguishability that is independent of the representation chosen for the quantum states. It induces a hierarchy of approximations for group function methods. The simplifications that occur in the calculation of matrix elements among p-orthogonal group functions are presented.