UC Berkeley

This work extends the previous development of new mathematical machinery for nonlinear operators acting on a vector space. Starting from the usual concept of inner product, we find that Hermitian, anti-Hermitian, and unitary nonlinear operators can be defined without bringing in the ideas of a dual vector space or adjoint operators. After looking briefly at how these general ideas might be used in classical mechanics and to extend the linear Schrodinger equation of quantum theory, the topic of Lie groups and Lie algebras is studied. Many, but not all, of the familiar features of that topic are extended to nonlinear operators. New representations are found for a few simple cases of interest to physics, and some provocative implications for elementary particle theory are discussed.