On a Gauge Invariant Quantum Formulation for Non-gauge Classical Theory

TL;DR

This paper introduces a gauge-invariant canonical formulation for non-gauge classical theories, demonstrating its application to bosonic string theory with background tachyonic fields and deriving the mass-shell condition.

Contribution

It presents a novel method to construct gauge-invariant canonical formulations for non-gauge theories, with restrictions on parameters ensuring algebra closure.

Findings

Mass-shell condition for tachyon derived within the new formulation

Restrictions on parameters for gauge invariance established

Application demonstrated in bosonic string theory context

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 for illustration to bosonic string theory coupled to background tachyonic field. It is shown that within the proposed canonical formulation the known mass-shell condition for tachyon is produced.