Gauge Theories Coupled to Fermions in Generation
Hiromi Kase, Katsusada Morita, Yoshitaka Okumura
TL;DR
This paper reformulates gauge theories with fermions using extended differential geometry, applies it to the standard model, and explores the Higgs mechanism's dependence on the number of generations.
Contribution
It introduces a modified geometric framework for gauge theories with fermions and analyzes the Higgs mechanism's behavior across different generations.
Findings
Higgs mechanism operates only for more than one generation
Framework successfully reformulates the standard model with Connes' real structure
Extended differential geometry provides new insights into gauge theories
Abstract
Gauge theories coupled to fermions in generation are reformulated in a modified version of extended differential geometry with the symbol . After discussing several toy models, we will reformulate in our framework the standard model based on Connes' real structure. It is shown that for the most general bosonic lagrangin which is required to also reconstruct N=2 super Yang-Mills theory Higgs mechanism operates only for more than one generation as first pointed out by Connes and Lott.
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