Sphere-like Solutions in Surface Functional Theory and Dirac's Membrane Model

A surface functional theory for p-dimensional extended objects, the p-branes, was proposed in previous papers. The field equations for toroidal p-branes was exactly solved in $d=p+2$ dimensions, yielding equally spaced mass-squared spectrum with massless states. In this paper, we obtain the asymptotic distribution of mass spectrum in the point-particle limit of the theory with sphere-like membranes ($p=2$) in $d=4$ dimensions. Similarity between this spectrum and that obtained in the Dirac's membrane model of electron is discussed.