Quantization of Non-Critical Bosonic Open String Theory

TL;DR

This paper develops a Lorentz-invariant quantization method for bosonic open string theory in four-dimensional Minkowski space, resulting in a consistent quantum model with Regge-like spectrum.

Contribution

It introduces a new gauge fixing and canonical variables enabling the first consistent Lorentz-invariant quantization of bosonic open strings in four dimensions.

Findings

Quantum theory has Regge-like spin-mass spectrum.

Quantization is achieved in Minkowski space-time of dimension 4.

New Lorentz-invariant canonical variables are constructed.

Abstract

The theory of relativistic strings is considered in frames of Hamiltonian formalism and Dirac's quantization procedure. A special gauge fixing condition is formulated, related with the world sheet of the string in Lorentz-invariant way. As a result, a new set of Lorentz-invariant canonical variables is constructed, in which a consistent quantization of bosonic open string theory could be done in Minkowski space-time of dimension $d=4$. The obtained quantum theory possesses spin-mass spectrum with Regge-like behavior.