An exact operator solution of the quantum Liouville field theory

Eric Braaten, Thomas Curtright, Charles Thorn

Research output: Contribution to journalArticle

128 Citations (Scopus)

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: ∂μΦ, and e. 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 languageEnglish (US)
Pages (from-to)365-416
Number of pages52
JournalAnnals of Physics
Volume147
Issue number2
DOIs
StatePublished - 1983
Externally publishedYes

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operators
conformal mapping
quantum theory
equivalence
eigenvectors
kinetic energy
tensors
products
energy

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

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

In: Annals of Physics, Vol. 147, No. 2, 1983, p. 365-416.

Research output: Contribution to journalArticle

Braaten, Eric ; Curtright, Thomas ; Thorn, Charles. / An exact operator solution of the quantum Liouville field theory. In: Annals of Physics. 1983 ; Vol. 147, No. 2. pp. 365-416.
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