Superconnections and internal supersymmetry dynamics.

In previous papers we proposed a theory of internal supersymmetry using the superalgebra su(n/1) to give rise to a unified structure that included quarks and leptons in 2n-5 generations. In the present paper we suggest that the notion of superconnections as introduced by Quillen provides a natural setting for the dynamics of an internally supersymmetric theory with the Higgs field occurring as the "zero-th order part" of the superconnection. The Higgs mechanism enters quadratically into the curvature of the superconnection and hence quartically into the Lagrangian. The supercovariant derivative gives a coupling of the Higgs field to the matter field similar to that put in "by hand" in the Lagrangian of the Weinberg-Salam theory.