An Exact Membrane Quantization from W(Infinity) Symmetry

Abstract

An exact quantization of the spherical membrane moving in flat target spacetime backgrounds is performed. Crucial ingredients are the exact integrabilty of the $3DSU(\infty )$ 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 pages

References in corpus (1)

• Unifying W-Algebras