Internal symmetry algebra of exactly integrable dynamical systems in the quantum domain

Journal Article · Thu Oct 01 00:00:00 EDT 1987 · Theor. Math. Phys.; (United States)

DOI:https://doi.org/10.1007/BF01029097· OSTI ID:5616929

Lesnov, A N; Mukhtarov, M A

For the example of the generalized Toda chain in two-dimensional space it is shown that in the quantum domain the semisimple algebras of the classical problem go over into the associative Hopf algebras described by Drinfel'd as quantum algebras. In terms of the quantum algebras, the Heisenberg operators of the interacting field can be expressed as functions of the in fields by means of the formulas of the classical theory, and the expressions obtained earlier for them acquire a simple algebraic meaning.

• Research Organization: Institute of High Energy Physics, Serpukhov, USSR
• OSTI ID: 5616929
• Journal Information: Theor. Math. Phys.; (United States), Vol. 71:1; Other Information: Translated from Theor. Mat. Fiz.; 71: No. 1, 46-53(Apr 1987)
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
QUANTUM FIELD THEORY
ALGEBRA
GROUP THEORY
SYMMETRY GROUPS
CLASSICAL MECHANICS
HEISENBERG PICTURE
LAGRANGIAN FUNCTION
QUANTIZATION
QUANTUM OPERATORS
SCALAR FIELDS
TWO-DIMENSIONAL CALCULATIONS
FIELD THEORIES
FUNCTIONS
MATHEMATICAL OPERATORS
MATHEMATICS
MECHANICS
645400* - High Energy Physics- Field Theory
657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics