TL;DR
This paper reviews quantum kinematics of identical particles, exploring new statistical possibilities beyond bosons and fermions in 2+1 dimensions, including anyons and nonabelian statistics, with implications for experimental realizations.
Contribution
It introduces new quantum statistical possibilities in lower dimensions and presents a spinor construction for nonabelian statistics with potential 3+1 dimensional extension.
Findings
Identification of new quantum statistics beyond bosons and fermions
Description of flux-charge constructions for abelian and nonabelian anyons
Proposal of a spinor construction for nonabelian statistics with higher-dimensional extension
Abstract
I review the quantum kinematics of identical particles, which suggests new possibilities, beyond bosons and fermions, in 2+1 dimensions; and how simple flux-charge constructions embody the new possibilities, leading to both abelian and nonabelian anyons. I briefly allude to experimental realizations, and also advertise a spinor construction of nonabelian statistics, that has a 3+1 dimensional extension.
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