A Possible Way of Connecting the Grassmann Variables and the Number of Generation

Abstract

We construct a Left-Right symmetric model in which the number of generation is related to Grassmann variables. We introduce two sets of complex Grassmann variables ($θ^1_q$,$θ^2_q$), ($θ^1_l$, $θ^2_l$) and associate each variable with left- and right-handed quark and lepton fields, respectively. Expanding quark and lepton fields in powers of the Grassmann variables, we find that there are exactly three generations of quarks and leptons. Integrating out the Grassmann variables, we obtain phenomenologically acceptable fermion mass matrices.