No labeling quantum mechanics of indiscernible particles

TL;DR

This paper introduces a new formalism called Q-space for quantum mechanics of indistinguishable particles, avoiding traditional labeling and tensor product formalism by focusing on occupation numbers and permutation invariance.

Contribution

It develops a novel vector space formalism for indistinguishable particles that bypasses labeling, aligning with the unobservability of permutations in quantum mechanics.

Findings

Q-space formalism successfully models indistinguishable particles without labels

Permutation operators act as identity in Q-space, reflecting physical indistinguishability

The approach aligns with quasi-set theory principles

Abstract

Our aim in this paper is to show an example of the formalism we have developed to avoid the label-tensor-product-vector-space-formalism of quantum mechanics when dealing with indistinguishable quanta. States in this new vector space, that we call the Q-space, refer only to occupation numbers and permutation operators act as the identity operator on them, reflecting in the formalism the unobservability of permutations, a goal of quasi-set theory.