A method of noncommutative integration of linear partial differential equations that is analogous to noncommutative integration of finite-dimensional Hamiltonian systems is proposed. The method is based on the concept, introduced in the paper, of a λ representation of Lie algebras. The method can be applied to the integration of the Klein-Gordon equation in Riemannian spaces of non-Stäckel type (i.e., in spaces that do not admit complete separation of the variables).
ASJC Scopus subject areas
- Mathematical Physics
- Statistical and Nonlinear Physics