GENERALIZED GAUGE TRANSFORMATIONS AND HIDDEN SYMMETRY IN THE STANDARD MODEL

Abstract

A recently proposed, new construction of the Standard Model based on the graded Lie algebra SU (2|1) is analyzed in some depth. The essential ingredient is an algebraic superconnection which incorporates both the gauge fields and the Higgs fields and whose curvature automatically leads to a spontaneously broken realization of the theory. The mechanism of hiding the original algebraic structure is unorthodox and is due to the specific, "noncommutative" realization of SU (2|1). The model is characterized by a constant background supercurvature which is invariant under arbitrary, constant SU (2|1) gauge transformations. This background field whose effect is analogous to the action of a constant magnetic field on a spherical atom, is traced back to the differential in the space of (super)matrices by means of which the supercurvature is constructed. The same background field is responsible for the fact that the ground state has no more than the U (1) e.m. symmetry of electromagnetism, the SU (2)L × U (1) symmetry of the Standard Model being recovered only after "backshifting" the Higgs fields. Thus, the Higgs mechanism receives a new and geometrical interpretation.