A Family of unitary higher order equations

TL;DR

This paper explores higher order wave equations for scalar fields, demonstrating their equivalence to multiple second order theories and establishing their renormalizability and unitarity.

Contribution

It introduces a family of higher order Lorentz invariant wave equations and proves their equivalence to multiple second order theories, along with their renormalizability and unitarity.

Findings

Higher order theories are equivalent to n independent second order theories.

Theories are proven to be renormalizable and unitary for any order n.

Matrix elements reduce to the Klein-Gordon case for charged particles.

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 proved that the $ n^{th} $ 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.