Quantum Strings and Superstrings

TL;DR

This paper presents a rigorous construction of quantum bosonic and superstring systems, proving equivalence of quantization methods and simplifying BRST quantization without vertex algebras.

Contribution

It introduces a new elementary approach to string quantization, including DDF operators, and provides simplified proofs of key equivalences and quantization procedures.

Findings

Constructed quantum bosonic and supersymmetric string systems.

Proved equivalence between light-cone and covariant quantization.

Simplified the proof of BRST quantization.

Abstract

In the first sections of this paper we give an elementary but rigorous approach to the construction of the quantum Bosonic and supersymmetric string system continuing the analysis of Dimock. This includes the construction of the DDF operators without using the vertex algebras. Next we give a rigorous proof of the equivalence between the light-cone and the covariant quantization methods. Finally, we provide a new and simple proof of the BRST quantization for these string models.