### 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) |
---|---|

Pages (from-to) | 4056-4072 |

Number of pages | 17 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 40 |

Issue number | 12 |

DOIs | |

State | Published - 1989 |

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### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

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

**Modular invariance and stochastic quantization.** / Ordez, Carlos R.; Rubin, Mark A.; Zwanziger, Daniel.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 40, no. 12, pp. 4056-4072. https://doi.org/10.1103/PhysRevD.40.4056

}

TY - JOUR

T1 - Modular invariance and stochastic quantization

AU - Ordez, Carlos R.

AU - Rubin, Mark A.

AU - Zwanziger, Daniel

PY - 1989

Y1 - 1989

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=35949012189&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35949012189&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.40.4056

DO - 10.1103/PhysRevD.40.4056

M3 - Article

VL - 40

SP - 4056

EP - 4072

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 12

ER -