The anticommutator spin algebra, its representations and quantum group invariance

TL;DR

This paper introduces a new algebra based on anticommutators, explores its representations, and demonstrates its invariance under a specific quantum group, expanding understanding of algebraic structures in quantum physics.

Contribution

It defines a novel anticommutator-based algebra, characterizes its representations, and establishes its invariance under the quantum group SO_q(3) at q=-1.

Findings

Integer spin representations correspond to angular momentum algebra

Half-integer spin representations split into two of dimension j+1/2

The algebra is invariant under SO_q(3) with q=-1

Abstract

We define a 3-generator algebra obtained by replacing the commutators by anticommutators in the defining relations of the angular momentum algebra. We show that integer spin representations are in one to one correspondence with those of the angular momentum algebra. The half-integer spin representations, on the other hand, split into two representations of dimension j + 1/2. The anticommutator spin algebra is invariant under the action of the quantum group SO_q(3) with q=-1.