Altering the Symmetry of Wavefunctions in Quantum Algebras and Supersymmetry

TL;DR

This paper explores the connection between wavefunction symmetry alterations in quantum algebras at the limit q=-1 and supersymmetry, suggesting a potential underlying supersymmetric structure in SU(2)_q.

Contribution

It proposes a novel perspective linking symmetry-altering operators in quantum groups to supersymmetric theories, supported by heuristic comparisons and implications for invariant Hamiltonian construction.

Findings

Statistics-altering operators at q=-1 resemble supersymmetry operators.

Alternating-symmetry multiplets may be key to constructing invariant Hamiltonians.

Potential underlying supersymmetry structure in SU(2)_q at the limit q=-1.

Abstract

The statistics-altering operators present in the limit $q=-1$ of multiparticle SU_q(2)-invariant subspaces parallel the action of such operators which naturally occur in supersymmetric theories. We illustrate this heuristically by comparison to a toy $N=2$ superymmetry algebra, and ask whether there is a supersymmetry structure underlying SU(2)_q at that limit. We remark on the relevance of such alternating-symmetry multiplets to the construction of invariant hamiltonians.