### Abstract

Two independent weak-coupling expansions are developed for the Liouville quantum field theory on a circle. In the first, the coupling of the nonzero modes is treated as a perturbation on the exact solution to the zero-mode problem (quantum mechanics with an exponential potential). The second approach is a weak-coupling approximation to an explicit operator solution which expresses various Liouville operators as functions of a free massless field using a Bäcklund transformation. It is shown that the free state space associated with the latter solution must be restricted to the sector which is odd with respect to a type of "parity." Various matrix elements are computed to order g^{10} using both approaches, yielding identical results.

Original language | English (US) |
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Pages (from-to) | 147-201 |

Number of pages | 55 |

Journal | Annals of Physics |

Volume | 153 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1984 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Annals of Physics*,

*153*(1), 147-201. https://doi.org/10.1016/0003-4916(84)90187-8