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Title: On the operator solution of the Liouville theory

Abstract

Using quantized self dual fields, the authors present an explicit operator solution to the Liouville theory, and discuss the results. The Liouville theory presents many problems; it is known to be integrable, and the authors aim at an explicit solution. In the literature, there are excellent works dealing with operator solutions to this theory. The authors claim that the present solution has the advantage giving the Liouville field Phi directly in terms of known fields, whose Fourier expansion is well-defined and is given in terms of creation and annihilation operators. A quantum Backlund transformation is constructed, providing a nonlinear relation between the Liouville field and a free field. A solution for the model in a strip of width ..pi.. is presented, a problem relevant to open strings. It is very important, especially in string theory, to have an explicit solution to the Liouville theory, since it describes the conformal anomaly, if one shifts the dimension away from the critical value. The classical theory has been studied in considerable detail. The point the authors use in the construction is the inverse map.

Authors:
;  [1]
  1. Instituto de Fisica, Universidade de Sao Paulo, C.P. 20516, Sao Paulo (BR)
Publication Date:
OSTI Identifier:
6389084
Resource Type:
Journal Article
Journal Name:
Mod. Phys. Letters B; (United States)
Additional Journal Information:
Journal Volume: 3:16
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANNIHILATION OPERATORS; FOURIER TRANSFORMATION; CLASSICAL MECHANICS; LIOUVILLE THEOREM; STRING MODELS; FIELD EQUATIONS; NONLINEAR PROBLEMS; COMPOSITE MODELS; EQUATIONS; EXTENDED PARTICLE MODEL; INTEGRAL TRANSFORMATIONS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; MECHANICS; PARTICLE MODELS; QUANTUM OPERATORS; QUARK MODEL; TRANSFORMATIONS; 645400* - High Energy Physics- Field Theory; 657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics

Citation Formats

Abdalla, E, and Santos, A L. On the operator solution of the Liouville theory. United States: N. p., 1988. Web. doi:10.1142/S0217732388001884.
Abdalla, E, & Santos, A L. On the operator solution of the Liouville theory. United States. https://doi.org/10.1142/S0217732388001884
Abdalla, E, and Santos, A L. 1988. "On the operator solution of the Liouville theory". United States. https://doi.org/10.1142/S0217732388001884.
@article{osti_6389084,
title = {On the operator solution of the Liouville theory},
author = {Abdalla, E and Santos, A L},
abstractNote = {Using quantized self dual fields, the authors present an explicit operator solution to the Liouville theory, and discuss the results. The Liouville theory presents many problems; it is known to be integrable, and the authors aim at an explicit solution. In the literature, there are excellent works dealing with operator solutions to this theory. The authors claim that the present solution has the advantage giving the Liouville field Phi directly in terms of known fields, whose Fourier expansion is well-defined and is given in terms of creation and annihilation operators. A quantum Backlund transformation is constructed, providing a nonlinear relation between the Liouville field and a free field. A solution for the model in a strip of width ..pi.. is presented, a problem relevant to open strings. It is very important, especially in string theory, to have an explicit solution to the Liouville theory, since it describes the conformal anomaly, if one shifts the dimension away from the critical value. The classical theory has been studied in considerable detail. The point the authors use in the construction is the inverse map.},
doi = {10.1142/S0217732388001884},
url = {https://www.osti.gov/biblio/6389084}, journal = {Mod. Phys. Letters B; (United States)},
number = ,
volume = 3:16,
place = {United States},
year = {Tue Nov 01 00:00:00 EST 1988},
month = {Tue Nov 01 00:00:00 EST 1988}
}