The theory of Lie algebras and their classification based on Dynkin diagrams is reviewed and application of the theory to vector wave scattering and propagation is outlined. The main applications arise through the matrix exponential function and associated matrix representations for the underlying groups. By projecting experimental measurements onto the eigenvectors of these basis elements, clear physical significance may be attached to the propagation operators. A new method for dealing with partially coherent propagators is outlined and an example for backscatter from a cloud of dipoles is used to illustrate the technique.