Applications of the concept of strength of a system of partial differential equations

Abstract

The concept of ``strength'' of a system of field equations was introduced by Einstein, and is of such generality that one can compare vastly different systems of field equations. We review here this concept in arbitrary number of dimensions and apply it to some of the well-known equations of physics. We calculate the strength, in arbitrary dimensions, of massless Klein-Gordon equations, Maxwell equations (in both potential and field formulation), and Einstein equations. We also determine the strength of massless Dirac equation and Weyl's neutrino equation for the case of four dimensions. It turns out that the strength for all these equations is identical for space-time dimensionality of four. Other possible applications of this concept are indicated.