Modular Localization of Massive Particles with "Any" Spin in d=2+1

TL;DR

This paper constructs a localization framework for massive anyons in 2+1 dimensions, enabling a quantum field theory approach despite the absence of free fields, and establishes a PCT symmetry for these particles.

Contribution

It introduces an intrinsic localization structure for massive anyons with arbitrary spin, extending quantum field theory concepts to particles without free field representations.

Findings

Existence of a localization structure for massive anyons in 2+1 dimensions.

Explicit formulas for real subspaces associated with localization.

Proof of a single-particle PCT theorem with geometric action.

Abstract

We discuss a concept of particle localization which is motivated from quantum field theory, and has been proposed by Brunetti, Guido and Longo and by Schroer. It endows the single particle Hilbert space with a family of real subspaces indexed by the space-time regions, with certain specific properties reflecting the principles of locality and covariance. We show by construction that such a localization structure exists also in the case of massive anyons in d=2+1, i.e. for particles with positive mass and with arbitrary spin s in the reals. The construction is completely intrinsic to the corresponding ray representation of the (proper orthochronous) Poincare group. Our result is of particular interest since there are no free fields for anyons, which would fix a localization structure in a straightforward way. We present explicit formulas for the real subspaces, expected to turn out useful for the construction of a quantum field theory for anyons. In accord with well-known results, only localization in string-like, instead of point-like or bounded, regions is achieved. We also prove a single-particle PCT theorem, exhibiting a PCT operator which acts geometrically correctly on the family of real subspaces.