Algebraic Quantization of the Closed Bosonic String

 The gauge invariant observables of the closed bosonic string are quantized in four space-time dimensions by constructing their quantum algebra in a manifestly covariant approach, respecting all symmetries of the classical observables. The quantum algebra is the kernel of a derivation on the universal enveloping algebra of an infinite-dimensional Lie algebra. The search for Hilbert space representations of this algebra is separated from its construction, and postponed. Received: 26 February 2002 / Accepted: 5 September 2002 Published online: 28 March 2003 RID="⋆" ID="⋆" The article is based on the diploma thesis of the first author (C.M.) [1] under the supervision of K. Pohlmeyer, Universit?t Freiburg, completing a project by the second author (K.-H.R.) lying dormant since around 1987. RID="⋆⋆" ID="⋆⋆" Present address: Dept. of Mathematics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, UK. E-mail:C.Meusburger@ma.hw.ac.uk Communicated by H. Araki, D. Buchholz and K. Fredenhagen