2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149201An exact quantization of the spherical membrane moving in flat target spacetime backgrounds is performed. Crucial ingredients are the exact integrabilty of the $3D~SU(\infty)$ continuous Toda equation and the quasi-finite highest weight irreducible representations of $W_{\infty}$ algebras. Both continuous and discrete energy levels are found. The latter are found for periodic-like solutions. Membrane wavefunctionals solutions are found in terms of Bessel's functions and plausible relations to singleton field theory are outlined.15 pagesHigh Energy Physics - Theorytext