An exact operator solution of the quantum Liouville field theory

Eric Braaten, Thomas Curtright, Charles Thorn

Research output: Contribution to journalArticlepeer-review

130 Scopus citations


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
Issue number2
StatePublished - May 1983
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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