A Family of Unitary Higher Order Equations

Abstract

A scalar field obeying a Lorentz invariant higher order wave equation, is minimally coupled to the electromagnetic field. The propagator and vertex factors for the Feynman diagrams, are determined. As an example we write down the matrix element for the Compton effect. This matrix element is algebraically reduced to the usual one for a charged Klein–Gordon particle. It is proven that the nth order theory is equivalent to n independent second order theories. It is also shown that the higher order theory is both renormalizable and unitary for arbitrary n.