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An Exact Membrane Quantization from W(Infinity) Symmetry

Carlos Castro
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Abstract

An 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.

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Carlos Castro. 1995-04-25. An Exact Membrane Quantization from W(Infinity) Symmetry. https://arxiv.org/abs/hep-th/9504023

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