TL;DR
This paper provides an algebraic proof of the spin-statistics connection for parabosonic and parafermionic charges in local observable theories, applicable in 1+2 dimensions and avoiding spinor calculus.
Contribution
It introduces a novel algebraic proof of the spin-statistics relation that extends to lower dimensions and different types of quantum charges.
Findings
Proof avoids spinor calculus
Applicable in 1+2 dimensions
Progress towards a general spin-statistics theorem
Abstract
We give an algebraic proof of the spin-statistics connection for the parabosonic and parafermionic quantum topological charges of a theory of local observables with a modular PCT-symmetry. The argument avoids the use of the spinor calculus and also works in 1+2 dimensions. It is expected to be a progress towards a general spin-statistics theorem including also (1+2)-dimensional theories with braid group statistics.
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