Anyons in the operational formalism

Abstract

The operational formalism to quantum mechanics seeks to base the theory on a firm foundation of physically well-motivated axioms [1]. It has succeeded in deriving the Feynman rules [2] for general quantum systems. Additional elaborations have applied the same logic to the question of identical particles, confirming the so-called Symmetrization Postulate [3]: that the only two options available are fermions and bosons [4,5]. However, this seems to run counter to results in two-dimensional systems, which allow for anyons, particles with statistics which interpolate between Fermi-Dirac and Bose-Einstein (see [6] for a review).In this talk we will show that the results in two dimensions can be made compatible with the operational results. That is, we will show that anyonic behavior is a result of the topology of the space in two dimensions [7], and does not depend on the particles being identical; but that nevertheless, if the particles are identical, the resulting system is still anyonic.

Identical Particles in Quantum Mechanics: Operational and Topological Considerations

“…Using the operational understanding of the Symmetrization Postulate, we show that anyonic behavior is solely due to topology, rather than particle identicality. An overview of these results was presented as "Anyons in the Operational Formalism" at MaxEnt 2014 ¶ , published in its proceedings as Neori and Goyal [6]. The derivation of quantization in multiply-connected spaces using the fundamental groupoid, taken up in Chapter 3, was submitted for publication as Neori and Goyal [7].…”