Algebraic quantization of the closed bosonic string

Abstract

The gauge invariant observables of the closed bosonic string are quantized without anomalies in four space-time dimensions by constructing their quantum algebra in a manifestly covariant approach. The quantum algebra is the kernel of a derivation on the universal envelopping algebra of an infinite-dimensional Lie algebra. The search for Hilbert space representations of this algebra is separated from its construction, and postponed.