Dirac equation for strings

TL;DR

This paper derives a Dirac-like equation for strings from the Nambu-Goto action, resulting in a real spectrum free of tachyons, with exact solutions for certain oscillations.

Contribution

It introduces a novel Dirac-like formulation for string dynamics and provides exact solutions for specific oscillation modes.

Findings

Eigenvalues are real and correspond to string masses

No tachyonic states are present

Exact solutions for radial oscillations of closed strings

Abstract

Starting with a Nambu-Goto action, a Dirac-like equation can be constructed by taking the square-root of the momentum constraint. The eigenvalues of the resulting Hamiltonian are real and correspond to masses of the excited string. In particular there are no tachyons. A special case of radial oscillations of a closed string in Minkowski space-time admits exact solutions in terms of wave functions of the harmonic oscillator.