Nonlinear operators and their propagators (Q2785764)

The author develops a general algebra and calculus for nonlinear operators. The basic new tool is the ``slash product'' of two operators, \(A/B\), defined by \(A(1+\varepsilon B)=A+\varepsilon A/B+O(\varepsilon ^2)\). A number of properties of this quantity are explored. For a genetic time development equation the propagator is constructed. It is explored how the further machinery of quantum theory might look if it were not a linear theory. A nonperturbation approximation scheme capable of producing high accuracy computations, previously developed for linear operators, is shown to be applicable as well in the nonlinear domain. A number of mathematical results are given.