The Einstein-hilbert-yang-mills-higgs Action and the Dirac-yukawa Operator
نویسنده
چکیده
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. PACS-92 04.50 Unified field theories and other theories of gravitation 11.15 Gauge field theories MSC-91 81E13 Yang-Mills and other gauge theories 83E99 General relativity, unified field theories arch-ive/9612149
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