On the Origin of the Quantum Rules for Identical Particles

TL;DR

This paper provides a proof of the Symmetrization Postulate for noninteracting identical particles within the Feynman formalism, clarifying the foundational assumptions and improving upon previous derivations.

Contribution

It offers a clearer, more rigorous proof of the Symmetrization Postulate, avoiding strong assumptions and building on operational quantum mechanics principles.

Findings

Proof applies to noninteracting, identical particles

Improves upon Tikochinsky's derivation by clarifying assumptions

Avoids strong, abstract assumptions like analyticity

Abstract

We present a proof of the Symmetrization Postulate for the special case of noninteracting, identical particles. The proof is given in the context of the Feynman formalism of Quantum Mechanics, and builds upon the work of Goyal, Knuth and Skilling (Phys. Rev. A 81, 022109 (2010)), which shows how to derive Feynman's rules from operational assumptions concerning experiments. Our proof is inspired by an attempt to derive this result due to Tikochinsky (Phys. Rev. A 37, 3553 (1988)), but substantially improves upon his argument, by clarifying the nature of the subject matter, by improving notation, and by avoiding strong, abstract assumptions such as analyticity.