### Abstract

Exact, closed form results are given expressing the quantum Liouville field theory in terms of a canonical free pseudoscalar field. The classical conformal transformation properties and a Bäcklund transformation of the Liouville model are briefly reviewed and then developed into explicit operator statements for the quantum theory. This development leads to exact expressions for the basic operator functions of the Liouville field: ∂_{μ}Φ, and e^{nΦ}. An operator product analysis is then used to construct the Liouville energy-momentum tensor operator, which is shown to be equal to that of a free pseudoscalar field. Dynamical consequences of this equivalence are discussed, including the relation between the Liouville and free field energy eigenstates. Liouville correlation functions are partially analyzed, and remaining open questions are discussed.

Original language | English (US) |
---|---|

Pages (from-to) | 365-416 |

Number of pages | 52 |

Journal | Annals of Physics |

Volume | 147 |

Issue number | 2 |

DOIs | |

State | Published - 1983 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Annals of Physics*,

*147*(2), 365-416. https://doi.org/10.1016/0003-4916(83)90214-2

**An exact operator solution of the quantum Liouville field theory.** / Braaten, Eric; Curtright, Thomas; Thorn, Charles.

Research output: Contribution to journal › Article

*Annals of Physics*, vol. 147, no. 2, pp. 365-416. https://doi.org/10.1016/0003-4916(83)90214-2

}

TY - JOUR

T1 - An exact operator solution of the quantum Liouville field theory

AU - Braaten, Eric

AU - Curtright, Thomas

AU - Thorn, Charles

PY - 1983

Y1 - 1983

N2 - Exact, closed form results are given expressing the quantum Liouville field theory in terms of a canonical free pseudoscalar field. The classical conformal transformation properties and a Bäcklund transformation of the Liouville model are briefly reviewed and then developed into explicit operator statements for the quantum theory. This development leads to exact expressions for the basic operator functions of the Liouville field: ∂μΦ, and enΦ. An operator product analysis is then used to construct the Liouville energy-momentum tensor operator, which is shown to be equal to that of a free pseudoscalar field. Dynamical consequences of this equivalence are discussed, including the relation between the Liouville and free field energy eigenstates. Liouville correlation functions are partially analyzed, and remaining open questions are discussed.

AB - Exact, closed form results are given expressing the quantum Liouville field theory in terms of a canonical free pseudoscalar field. The classical conformal transformation properties and a Bäcklund transformation of the Liouville model are briefly reviewed and then developed into explicit operator statements for the quantum theory. This development leads to exact expressions for the basic operator functions of the Liouville field: ∂μΦ, and enΦ. An operator product analysis is then used to construct the Liouville energy-momentum tensor operator, which is shown to be equal to that of a free pseudoscalar field. Dynamical consequences of this equivalence are discussed, including the relation between the Liouville and free field energy eigenstates. Liouville correlation functions are partially analyzed, and remaining open questions are discussed.

UR - http://www.scopus.com/inward/record.url?scp=0000034770&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000034770&partnerID=8YFLogxK

U2 - 10.1016/0003-4916(83)90214-2

DO - 10.1016/0003-4916(83)90214-2

M3 - Article

AN - SCOPUS:0000034770

VL - 147

SP - 365

EP - 416

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

IS - 2

ER -