Graph theory and relativistic field equations for half odd integer spin and unique mass

Abstract

Graph theoretical methods are used to analyse relativistic field equations for half odd integer spin and unique mass. The analysis is easiest when repeated irreducible representations (RIR) of the Lorentz group do not occur, but the methods apply in general cases, and can also be used for equations with a mass-spin spectrum. A simple graph theoretical method for finding the possible minimal polynomials of L0 is given, and some general results on the possible structure of the equations are obtained. As an example, all theories of spin-5/2, without RIR, are considered and it is shown that there are none with unique mass. Theories with RIR are briefly discussed.