Algebraic quantization of the closed bosonic string

TL;DR

This paper presents an anomaly-free algebraic quantization of gauge-invariant observables for the closed bosonic string in four dimensions, using a covariant approach that separates algebra construction from representation theory.

Contribution

It introduces a novel covariant quantization method for the string's observables, avoiding anomalies and focusing on algebraic structure over Hilbert space representations.

Findings

Quantum algebra constructed without anomalies in four dimensions

Covariant approach preserves gauge invariance

Separation of algebra construction from representation analysis

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.