MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

MiS Preprint

Gauge Theories of Dirac Type

Jürgen Tolksdorf and Torsten Thumstädter


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.

Mar 23, 2005
Mar 23, 2005
MSC Codes:
51P05, 53C07, 70S05, 70S15, 83C22
02.40.Hw, 02.40.Ma, 03.50.Kk, 03.65.Sq, 04.20.Cv
clifford modules, dirac type operators, bundle reduction, spontaneous symmetry breaking, fermionic mass operator

Related publications

2006 Repository Open Access
Jürgen Tolksdorf and Torsten Thumstädter

Gauge theories of dirac type

In: Journal of mathematical physics, 47 (2006) 8, p. 082305