Field Theoretical Construction of an Infinite Set of Quantum Commuting Operators Related with Soliton Equations

摘要

The quantum version of an infinite set of polynomial conserved quantities of a class of soliton equations is discussed from the point of view of naive continuum field theory. By using techniques of two dimensional field theories, we show that an infinite set of quantum commuting operators can be constructed explicitly from the knowledge of its classical counterparts. The quantum operators are so constructed as to coincide with the classical ones in the Planck constant -> 0 limit (Planck constant; Planck's constant divided by 2 pi ). It is expected that the explicit forms of these operators would shed some light on the structure of the infinite dimensional Lie algebras which underlie certain class of quantum integrable systems. (ERA citation 13:023545)