A 3-DIMENSIONAL GAUGE-THEORY COUPLED TO FERMIONIC SCALARS AND VECTORS

By involving the group indices of an SU(2) gauge theory in three Eucli dean dimensions in the Lorentz transformation, one finds that the gaug e field can be decomposed into a scalar, vector and tensor field which mix under a gauge transformation. It is shown how this gauge field ca n be coupled to an O(3) spinor field whose transformation properties a llow one to decompose it into a fermionic scalar and a fermionic vecto r field. Radiative corrections must be done in a way that respects the dimensionality of the theory; it is demonstrated how operator regular ization can be used to this end by computing the temperature dependenc e of the eta function arising from spinors.