Proton-Neutron Mass Difference in a Unified Gauge Model of Leptons and Hadrons

We discuss some problems associated with the physical interpretation and the renormalization of the model devised by Weinberg which combines the SU(2)×U(1) gauge theory of leptons and the $\sigma$ model. Some of the problems we discuss are: (1) renormalization counterterms of this model, (2) complications due to the existence of two scalar multiplets which develop vacuum expectation values, (3) the proton-neutron mass difference in this model. We point out that in this model there is a "zeroth-order" relation connecting the proton-neutron mass difference and certain coupling constants. Departure from this relation in higher orders is computable and we discuss the one-loop correction to this relation.