Elementary Particles and the Signature of the Space-time Metric

Abstract

IT is well known that the Lorentz transformations of special relativity leave invariant the infinitesimal separation : where c is the velocity of light and (t,x,y,z) are the time and Cartesian space co-ordinates. Equation (1) is the metric of the four-dimensional Minkowski space-time, the signature of which is −2 (this being the number of positive terms minus the number of negative terms in a metric when expressed in diagonal form). The signature of a metric, when once decided, is an invariant under real co-ordinate transformations.