Covariant generation of vector gauge bosons in non-Abelian gauge theories

Abstract

In the last years considerable effort has been devoted to a unification of strong, weak and electromagnetic interactions. Generally, in Unified theories an extraordinary number of fields occur; therefore it would be desirable to somehow reduce them to a minimal number of fundamental fields. In this spirit, unified theories and dynamical symmetry breaking could lead to the idea of fermions as fundamental . On the other hand, unified models are gauge models, therefore it seems compulsory to study how to introduce gauge vector bosons in terms of other fundamental fields (~). The main point in this letter is that they are introduced in a covariant way, in contrast with earlier references (~). We have chosen the simple example of SU2. Our letter shows the primordial role played by the fermions in the general mechanism of generation of vector gauge bosons. In this line, a reinterpretation of the scalar quaternionic fields, as true gauge group transformation, allows us to track back the theory to a pure fermion theory with only global symmetry. Technical by-products of our scheme are: i) occurence of fermion and boson degrees of freedom, ii) the bosch degrees should be associated to a definite representation of the symmetry, iii) the symmetry must be realized nonlinearly (2). The above scheme can be carried out in general for other non-Abelian symmetries. This work will be presented in a separate and more detailed paper. Let us consider a symmetry gauge group G and some scalar fields that undergo the transformation law