Quantisation ideals of nonabelian integrable systems
А. В. Михайлов
Abstract
We consider dynamical systems on the space of functions taking values in a free associative algebra. The system is said to be integrable if it possesses an infinite dimensional Lie algebra of commuting symmetries. In this paper we propose a new approach to the problem of quantisation of dynamical systems, introduce the concept of quantisation ideals and provide meaningful examples.
Topics & Concepts
Integrable systemMathematicsAssociative propertyAlgebra over a fieldHomogeneous spacePure mathematicsLie algebraSpace (punctuation)Dynamical systems theoryComputer scienceQuantum mechanicsGeometryOperating systemPhysicsNonlinear Waves and SolitonsAdvanced Topics in AlgebraAlgebraic structures and combinatorial models