Gauge theories of Dirac type

A specific class of gauge theories is geometrically described in terms offermions. In particular, it is shown how the geometrical frame presentednaturally includes spontaneous symmetry breaking of Yang-Mills gauge theorieswithout making use of a Higgs potential. In more physical terms, it is shownthat the Yukawa coupling of fermions, together with gravity, necessarily yieldsa symmetry reduction provided the fermionic mass is considered as a globallywell-defined concept. The structure of this symmetry breaking is shown to becompatible with the symmetry breaking that is induced by the Higgs potential ofthe minimal Standard Model. As a consequence, it is shown that the fermionicmass has a simple geometrical interpretation in terms of curvature and that the(semi-classical)"fermionic vacuum" determines the intrinsic geometry ofspace-time. We also discuss the issue of "fermion doubling" in some detail andintroduce a specific projection onto the "physical sub-space" that is motivatedfrom the Standard Model.Comment: 50 pages, mistake in prop. 3.2 and its proof corrected, comments added, subsections adde