Gauge Theories of Dirac Type

TL;DR

This paper presents a geometric framework for gauge theories involving fermions, naturally incorporating spontaneous symmetry breaking and relating fermionic mass to space-time curvature without relying on a Higgs potential.

Contribution

It introduces a geometric description of gauge theories with fermions that explains symmetry breaking and fermionic mass in terms of curvature, aligning with Standard Model phenomena.

Findings

Fermionic mass relates to space-time curvature.

Spontaneous symmetry breaking occurs without a Higgs potential.

A projection method addresses fermion doubling.

Abstract

A specific class of gauge theories is geometrically described in terms of fermions. In particular, it is shown how the geometrical frame presented naturally includes spontaneous symmetry breaking of Yang-Mills gauge theories without making use of a Higgs potential. In more physical terms, it is shown that the Yukawa coupling of fermions, together with gravity, necessarily yields a symmetry reduction provided the fermionic mass is considered as a globally well-defined concept. The structure of this symmetry breaking is shown to be compatible with the symmetry breaking that is induced by the Higgs potential of the minimal Standard Model. As a consequence, it is shown that the fermionic mass has a simple geometrical interpretation in terms of curvature and that the (semi-classical)"fermionic vacuum" determines the intrinsic geometry of space-time. We also discuss the issue of "fermion doubling" in some detail and introduce a specific projection onto the "physical sub-space" that is motivated from the Standard Model.