Lie theory and separation of variables. 8. Semisubgroup coordinates for Ψtt - ∆2Ψ = 0

Abstract

We classify and study all coordinate systems which permit R-separation of variables for the wave equation in three space–time variables and such that at least one of the variables corresponds to a one-parameter symmetry group of the wave equation. We discuss 33 such systems and relate them to orbits of commuting operators in the enveloping algebra of the conformal group SO (3,2).