On the operator solution of the Liouville theory

Journal Article · Tue Nov 01 04:00:00 EST 1988 · Mod. Phys. Letters B; (United States)

DOI:https://doi.org/10.1142/S0217732388001884· OSTI ID:6389084

Abdalla, E; Santos, A L ^[1]

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1. Instituto de Fisica, Universidade de Sao Paulo, C.P. 20516, Sao Paulo (BR)

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.

• OSTI ID: 6389084
• Journal Information: Mod. Phys. Letters B; (United States), Journal Name: Mod. Phys. Letters B; (United States) Vol. 3:16; ISSN MPLBE
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANNIHILATION OPERATORS
CLASSICAL MECHANICS
COMPOSITE MODELS
EQUATIONS
EXTENDED PARTICLE MODEL
FIELD EQUATIONS
FOURIER TRANSFORMATION
INTEGRAL TRANSFORMATIONS
LIOUVILLE THEOREM
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MECHANICS
NONLINEAR PROBLEMS
PARTICLE MODELS
QUANTUM OPERATORS
QUARK MODEL
STRING MODELS
TRANSFORMATIONS