My goal is to reproduce the fermions of the Standard Model with a Dirac field-equation in eight flat dimensions, where the particles are trapped in the four higher dimensions by a potential. The potential's form is taken to be a symmetric harmonic-oscillator in order to generate SU(4) quantum numbers, which in an SU(3)xU(1) decomposition can accommodate the SU(3) quantum numbers of quarks and leptons, as well as their U(1) generation-numbers. There are some indications that this trapping mechanism can be supplied by a soliton generated by a nonlinearity in the underlying field equations.
Over the years there has been some slow convergence of my approach with popular theories like string theory or M-theory. However, my model has not been developed as extensively as those theories, and differs from them in that the extra dimensions are taken to be flat (infinite in extent) and gravity is not considered to be relevant. Furthermore, bosons are assumed to be of a different origin than Dirac particles, so supersymmetry is not employed.
I consider the origin of elementary particles to be one of the great unanswered questions of modern physics. What kind of world do we live in? Are there extra dimensions? If so, do they stretch out to infinity, where one might find other universes and strange new physics? Or, are the extra dimensions curled up into tiny circles which are only apparent to us from the elementary particles' quantum numbers, footprints left in the web of space-time
