A Geometric Approach to the Standard Model

A geometric approach to the standard model in terms of the Clifford algebra $$ is advanced. The gauge symmetries and charge assignments of the fundamental fermions are seen to arise from a simple geometric model involving extra space-like dimensions. The bare coupling constants are found to obey $g_s\mathrm{/}g=1$ and $g^{\mathrm{\prime }}\mathrm{/}g=\sqrt{3\mathrm{/}5}$, consistent with SU(5) grand unification but without invoking the notion of master groups. In constructing the Lagrangian density terms, it is found that the Higgs isodoublet field emerges in a natural manner. A matrix representation of $$ is included as a computational aid.