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.