The extended Yang-Mills gauge theory in Euclidean space is a renormalizable (by power counting) gauge theory describing a local interacting theory of scalar, vector, and tensor gauge fields (with maximum spin 2). In this article we study the quantum aspects and various generalizations of this model in Euclidean space. In particular, the quantization of the pure gauge model in a. common class of covariant gauges is performed. We generalize the pure gauge sector by including matter fermions in the adjoint representation of the gauge group and analyze its N = 1 and N = 2 supersymmetric extensions. We show that the maximum half-integer spin contained in these fermion fields in dimension 4 is 3/2. Moreover, we develop an extension of this theory which will include internal gauge symmetries and the coupling to bosonic matter fields. The spontaneous symmetry breaking of the extended gauge symmetry is also analyzed. (C) 2001 Academic Press.
