On first order wave equations for elementary particles without subsidiary conditions

Abstract

The possibility of extending the application of the formalism used for the electron and meson fields, as developed from the equation $\partial _{k}\beta ^{k}\psi $ = i$\kappa \psi $ to other types of field, is investigated. It is shown that, subject to the conditions that (1) the equations must contain no subsidiary conditions, (2) either the total energy must be positive definite, or it must be possible to quantize the equations according to Fermi statistics without using an indefinite metric in Hilbert space, no such extension is possible.