### Abstract

In Polyakov path integrals and covariant closed-string field theory, integration over Teichmüller parameters must be restricted by hand to a single modular region. This problem has an analog in Yang-Mills gauge theorynamely, the Gribov problem, which can be resolved by the method of stochastic gauge fixing. This method is here employed to quantize a simple modular-invariant system: the Polyakov point particle. In the limit of a large gauge-fixing force, it is shown that suitable choices for the functional form of the gauge-fixing force can lead to a restriction of Teichmüller integration to a single modular region. Modifications which arise when applying stochastic quantization to a system in which the volume of the orbits of the gauge group depends on a dynamical variable, such as a Teichmüller parameter, are pointed out, and the extension to Polyakov strings and covariant closed-string field theory is discussed.

Original language | English (US) |
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Pages (from-to) | 4056-4072 |

Number of pages | 17 |

Journal | Physical Review D |

Volume | 40 |

Issue number | 12 |

DOIs | |

State | Published - Jan 1 1989 |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)

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## Cite this

*Physical Review D*,

*40*(12), 4056-4072. https://doi.org/10.1103/PhysRevD.40.4056