Fermi-Dirac Equations

Abstract

Assuming that space-time is accompanied by hidden anticommuting coordinates, we have constructed 'fermionic' eneralisations of the Dirac equation; these equations involve matrices (which can be construed as operating in an internal space) multiplying the Grassmann derivatives. We discuss several models, of varying degrees of complexity, with 'internal symmetries' including Sp(2) and S (N). By appending the space-time Dirac operator, one is led to mass spectra with quantised alues, suggesting that this approach may provide a model relating generations to internal symmetries.