Integrals of Motion and Quantum Groups

Details Integrals of Motion and Quantum Groups Integrals of Motion and Quantum Groups

1993-10-04

arxiv.org/abs/hep-th/9310022v3

Physics

High Energy Physics

High Energy Physics - Theory

71 pages (final version, to appear in Lect. Notes in Math, vol. 1620)

Scientific paper

A homological construction of integrals of motion of the classical and quantum Toda field theories is given. Using this construction, we identify the integrals of motion with cohomology classes of certain complexes, which are modeled on the BGG resolutions of the associated Lie algebras and their quantum deformations. This way we prove that all classical integrals of motion can be quantized. For the Toda field theories associated to finite-dimensional Lie algebras, the algebra of integrals of motions is the corresponding W-algebra. For affine Toda field theories this algebra is a commutative subalgebra of a W-algebra; it consists of quantum KdV hamiltonians.

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