Geometric Measure of Indistinguishability for Groups of Identical Particles

TL;DR

This paper introduces a geometric measure called p-orthogonality to quantify indistinguishability among groups of identical particles, generalizing existing orthogonality concepts and aiding in quantum state analysis.

Contribution

It defines p-orthogonality as a new geometric measure of indistinguishability, extending previous orthogonality notions and providing a hierarchy of approximations for group function methods.

Findings

Introduces p-orthogonality as a measure of indistinguishability.

Provides a geometric interpretation independent of state representation.

Simplifies calculations of matrix elements between p-orthogonal group functions.

Abstract

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 new hierarchy of approximations for group function methods. The simplifications that occur in the calculation of matrix elements between p-orthogonal group functions are presented.