Relativistic Quantum Field Theory of High-Spin Matter Fields: A Pragmatic approach for Hadronic Physics

Abstract

A consistent phenomenology of the interaction of particles of arbitrary spin requires covariant spinors, field operators, propagators and model interactions. Guided by an approach originally proposed by Weinberg, we construct from group theoretical arguments the (j,0)+(0,j) covariant spinors and the field operators for a massive particles. Specific examples are worked out in the familiar language of the Bjorken and Drell text for the case of the (1,0)+(0,1), (3/2,0)+(0,3/2) and (2,0)+(0,2) matter fields. The m\to 0 limit of the covariant spinors is shown to have the expected structure. The algebra of the γ^{μν} matrices associated with the (1,0)+(0,1) matter fields is presented, and the conserved current derived. The procedure readily extends to higher spins. The causality problem associated with the j\ge 1 wave equations is discussed in detail and a systematic procedure to construct causal propagators is provided. As an example a spin two wave equation satisfied by the (2,0)+(0,2), covariant spinors is found to support not only ten correct and causal solutions, but also thirty physically unacceptable acausal solutions. However, we demonstrate how to construct the Feynman propagator for the higher spin particles directly from the spinors and thus avoid the shortcomings of the wave equation in building a phenomenology. The same exercise is repeated for the (1,0)+(0,1) and (3/2,0)+(0,3/2) matter fields, and the same conclusions obtained. Massless limit is discussed in detail. (Typos uncorrected, Part of the work published and extended in several journal articles, for an important correction see physics/9702005).