Generalized Gauge Theories and the Weinberg–salam Model With Dirac–kähler Fermions

Abstract

We extend the previously proposed generalized gauge theory formulation of the Chern-Simons type and topological Yang-Mills type actions into Yang-Mills type actions. We formulate gauge fields and Dirac-Kähler matter fermions by all degrees of differential forms. The simplest version of the model which includes only zero and one-form gauge fields accommodated with the graded Lie algebra of SU(2|1) supergroup leads the Weinberg-Salam model. Thus the Weinberg-Salam model formulated by noncommutative geometry is a particular example of the present formulation. ‡ Present address: High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan. 3867 Int. J. Mod. Phys. A 2001.16:3867-3895. Downloaded from www.worldscientific.com by UNIVERSITY OF PITTSBURGH on 02/05/15. For personal use only.

Dirac–kähler Fermion From Clifford Product With Noncommutative Differential Form on a Lattice

“…It is interesting to point out that the Weinberg-Salam model was formulated by using the generalized gauge theory [5] with a graded Lie algebra of super group [55]. In this formulation the Clifford product was crucial in defining Yang-Mills action of generalized gauge theory and the introduction of Dirac-Kähler matter fermion.…”