Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-12-13
J.Math.Phys. 39 (1998) 2213-2241
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX, 39 pages, replacement of Dec. 20th with corrections in the second part, see eq.'s (164-169)
Scientific paper
10.1063/1.532284
In this article we show in some detail how the full action functional of the standard model of elementary particle physics can be described within the geometrical setting of generalized Dirac operators. We thereby introduce a new model building kit for (a certain class of) gauge invariant theories which provides a unified geometrical description of Einstein's theory of gravity and Yang-Mills gauge theories on the "classical" level. Moreover, when the gauge symmetry is spontaneously broken, the Higgs sector as well has a natural geometrical interpretation. It turns out that the Higgs field is related to the gravitational potential. Since the full action functional of the standard model is derived in one stroke, the appropriate parameters of the model have to satisfy certain relations similar to those in the Connes-Lott approach. Likewise, this may yield some phenomenological consequences, which is illustrated by using the gauge group of the standard model in the case of $N-$generations of leptons and quarks.
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