On the origin of the quantum rules for identical particles

Abstract

Ensemble fluctuations and the origin of quantum probabilistic rule Some general commutation rules and identities for three-dimensional quantum-mechanical operators Am.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 [1], 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 [2], 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.

Identical Particles in Quantum Mechanics: Operational and Topological Considerations

“…The basic idea of approaching identical particles from Refs. [1,2] completely sidesteps any criticism of the legitimacy of using particle labels, and does not result in a curved configuration space. Instead, it assumes that a certain problem has been solved for distinguishable particles, that is, with particle labels, and sees what consistent ways there are to combine these solutions into a solution to the identified system.…”

“…The research reported in Neori and Goyal [2] and Goyal [1] was able to overcome the dependence on analyticity. Additionally, one of the implicit assumptions in Ref.…”

“…Section 2.5, in particular, refers to an operational proof of this postulate published in Goyal [1]. Preliminary results focusing on the non-interacting, two-particle case were presented as "On the Origin of the Quantum Rules for Identical Particles" at QTRF-6 ‡ and MaxEnt 2012 § , and published in the proceedings of the latter as Neori and Goyal [2]. As explained in Ref.…”

“…We were able to improve upon the rigor of that result by starting from the operational approach to reconstructing the Feynman rules developed in Goyal et al [28]. We published preliminary results, for two non-interacting particles, in Neori and Goyal [2]. A generalization to N interacting particles can be found in Goyal [1].…”

“…[26], namely, that the amplitude for an identical particle transition had a functional dependence on the single-particle amplitudes, was made explicit in the special case of two, non-interacting particles in Ref. [2]. In Ref.…”