Theory of High-Spin Fields

Abstract

A general method for the construction of wave functions and wave equations for higher spins is proposed. This method is based on the full use of projection operators, without any use of boosting and without explicit use of auxiliary fields. The wave equations are always expressed in the form of single matrix equations, so that their Lagrangians follow immediately. Then the entire program of quantization of the free fields can follow straightforwardly by using the so-called $d\left(\partial \right)$-operator technique which was developed previously. The present method is made up of two steps: The first step is to derive wave equations when the maximum spin is specified; the second step is to derive equations when the spin itself is specified. The techniqu employed in the first step, when it is applied to many-spinor representations, can be used to put the Bargmann-Wigner equations into the form of a single matrix equation. The same technique enables us to write explicitly the Harish-Chandra $\beta$ matrices in terms of Dirac matrices. General arguments explain why the relativistic wave equations in general contain a certain number of arbitrary parameters, such as have been observed by several authors. The method is illustrated by several examples of relativistic wave equations.