A supersymmetric extension of quantum gauge theory

Abstract

We consider a supersymmetric extension of quantum gauge theory based on a vector multiplet containing supersymmetric partners of spin 3/2 for the vector fields. The constructions of the model follows closely the usual construction of gauge models in the Epstein-Glaser framework for perturbative field theory. Accordingly, all the arguments are completely of quantum nature without reference to a classical supersymmetric theory.As an application we consider the supersymmetric electroweak theory. The resulting self-couplings of the gauge bosons agree with the standard model up to a divergence.

The quantum supersymmetric vector multiplet and some problems in non-Abelian supergauge theory

“…for some supersymmetric Wick polynomial T . This hypothesis makes possible the generalization of the Epstein-Glaser approach to the supersymmetric case as it is showed in [14].…”

Quantum extended supersymmetries

“…We remind here the definition of a extended supersymmetric theory in a pure quantum context. We use the notations from [12].…”

“…The notion of irreducibility can be defined for any supersymmetric multiplet if we consider the quantum fields as a modulus over the ring of partial differential operators. As emphasized in [12], the matrix-valued operators p and q are subject to some constraints which generalize the case N = 1 (see [12] and [13]).…”

“…One can associate with every field of the multiplet from Theorem 3.1 a superfield using a sandwich formula as in [12] and [13]: if f is any field of the multiplet we define:…”

“…In two preceding papers [12,13] we have examined critically the possible supersymmetric extensions of the standard model for the case of un-extended supersymmetry i.e. N = 1.…”