Gauge theories of Dirac type

Journal Article · Tue Aug 15 04:00:00 EDT 2006 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2218673· OSTI ID:20860763

Tolksdorf, Juergen; Thumstaedter, Torsten ^[1]

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1. Max Planck Institute of Mathematics in the Sciences, Leipzig (Germany)

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 (semiclassical) '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 subspace' that is motivated by the Standard Model.

• OSTI ID: 20860763
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 8 Vol. 47; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DIRAC EQUATION
FERMIONS
GAUGE INVARIANCE
GRAVITATION
HIGGS BOSONS
HIGGS MODEL
MASS
QUANTUM GRAVITY
SEMICLASSICAL APPROXIMATION
SPACE-TIME
STANDARD MODEL
SUPERSYMMETRY
SYMMETRY BREAKING
YANG-MILLS THEORY
YUKAWA POTENTIAL