Unified Treatment of Gauge and Higgs Fields in Non-Commutative Differential Geometry

概要

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The generalized field strength in Chamseddine et al.'s formulation of non-commutative geometry used to reconstruct spontaneously broken gauge theories consists of two separately gauge covariant terms which are two- and zero-forms in the Clifford algebra. It is shown that a similar decomposition also exists in our previous formulation of the non-commutative differential geometry which, therefore, admits a generalized field strength no longer homogeneous in the degree of generalized forms. It turns out, however, that the Higgs potential in the present formalism is generated only from the homogeneous part of degree 2. This results in different origins of the Higgs potential in the two methods because, in Chamseddine et al.'s formalism, the potential comes from the zero-form assuming generation mixing among fermions. Several examples of broken gauge theories including SU(5) GUT in the bosonic sector are considered in the present formalism of the non-commutative differential geometry. In particular, the full SU(5) Higgs potential is recovered in contrast with the previous result which reproduced only part of it.
理論物理学刊行会の論文
1995-06-25