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Title: Exact operator solution of the quantum Liouville field theory

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 Baechlund 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: partial/sub ..mu../Phi, and e/sup n/phi. 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 equilvalence 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.

Authors:
; ;
Publication Date:
Research Org.:
Physics Department, University of Florida, Gainesville, Florida 32611
OSTI Identifier:
5720251
DOE Contract Number:  
AS05-81ER40008
Resource Type:
Journal Article
Journal Name:
Ann. Phys. (N.Y.); (United States)
Additional Journal Information:
Journal Volume: 147:2; Journal Issue: 2
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; QUANTUM FIELD THEORY; CANONICAL TRANSFORMATIONS; COMMUTATORS; ENERGY-MOMENTUM TENSOR; BAECKLUND TRANSFORMATION; BOUNDARY CONDITIONS; COMMUTATION RELATIONS; CORRELATION FUNCTIONS; FIELD EQUATIONS; LIOUVILLE THEOREM; QUANTUM OPERATORS; EQUATIONS; FIELD THEORIES; FUNCTIONS; MATHEMATICAL OPERATORS; TENSORS; TRANSFORMATIONS; 645400* - High Energy Physics- Field Theory

Citation Formats

Braaten, E, Curtright, T, and Thorn, C. Exact operator solution of the quantum Liouville field theory. United States: N. p., 1983. Web. doi:10.1016/0003-4916(83)90214-2.
Braaten, E, Curtright, T, & Thorn, C. Exact operator solution of the quantum Liouville field theory. United States. https://doi.org/10.1016/0003-4916(83)90214-2
Braaten, E, Curtright, T, and Thorn, C. 1983. "Exact operator solution of the quantum Liouville field theory". United States. https://doi.org/10.1016/0003-4916(83)90214-2.
@article{osti_5720251,
title = {Exact operator solution of the quantum Liouville field theory},
author = {Braaten, E and Curtright, T and Thorn, C},
abstractNote = {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 Baechlund 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: partial/sub ..mu../Phi, and e/sup n/phi. 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 equilvalence 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.},
doi = {10.1016/0003-4916(83)90214-2},
url = {https://www.osti.gov/biblio/5720251}, journal = {Ann. Phys. (N.Y.); (United States)},
number = 2,
volume = 147:2,
place = {United States},
year = {Sun May 01 00:00:00 EDT 1983},
month = {Sun May 01 00:00:00 EDT 1983}
}