Remarks on SU_q(2) fermions

TL;DR

This paper critically examines the use of SU_q(2) fermions in statistical mechanics and quantum field theory, identifying errors in previous assumptions about their relation to undeformed fermions and establishing new constraints.

Contribution

It corrects misconceptions in the literature regarding the connection between deformed and undeformed fermion operators in SU_q(2) frameworks.

Findings

Most applications based on incorrect assumptions are invalidated.

Constraints on the form of the relation between deformed and undeformed fermions are established.

Certain classes of ansatz are excluded based on the analysis.

Abstract

We show that most of the applications of SU_q(2) fermions to statistical mechanics and quantum field theory, previously discussed in literature, are based on a wrong statement about the connection between deformed and undeformed fermion operators. Then we exclude various classes of ansatz and we put some constraints about the form of such relation.