On a Canonical Formulation of String Theory in Massive Background Fields

TL;DR

This paper develops a gauge-invariant canonical framework for string theory in massive backgrounds, deriving linear equations of motion for background fields through algebra closure conditions.

Contribution

It introduces a novel canonical formulation method for non-gauge theories and applies it to bosonic string theory with massive backgrounds, ensuring gauge invariance and correct equations of motion.

Findings

Derived linear equations of motion for background fields

Established restrictions on parameters for gauge algebra closure

Provided a consistent canonical formulation for massive background fields

Abstract

We propose a method of constructing a gauge invariant canonical formulation for non-gauge classical theory which depends on a set of parameters. Requirement of closure for algebra of operators generating quantum gauge transformations leads to restrictions on parameters of the theory. This approach is then applied to bosonic string theory coupled to massive background fields. It is shown that within the proposed canonical formulation the correct linear equations of motion for background fields arise.