Quantized Weak Neutral Charge in Electroweak Interaction and a Possible GUT Group for Fundamental Force Unification

Abstract

The topics relevant to grand unified theories (GUT) for fundamental forces have been investigated in the literature for four decades. The possible quantization of weak neutral charge is suggested within the model of electroweak unification in this paper, and based on this scheme, a theoretical weak mixing angle (sin2θw = 3/13 = 0.230769…), which agrees well with experimental measurements, can be obtained. In order to explore the origin of quantized weak neutral charge, a model of SU(7) grand unification is proposed. We will show that in the SU(N) GUT, N must be at least 7 in order to interpret such a theoretical weak mixing angle. It can be found that under proper weak mixing conditions for diagonal (neutral) gauge fields, such a theoretical weak mixing angle can be derived. Some relevant topics such as gauge-field vielbein and adjoint vielbein are discussed. Though there are still many problems that have not been resolved, the present scenario would enable us to gain insight into relevant topics such as gauge symmetry breaking, electroweak force unification as well as grand unification.