Phenomenological approach to high-spin quantum fields based on the Weinberg formalism

Abstract

We investigate the possibility of constructing a covariant phenomenology of high-spin particles based on the work of Weinberg. We put forth a simple algebraic method for investigating the dispersion relations E=E(p,m) satisfied by the solutions to the free-particle Weinberg equations. We find that these equations support solutions which do not satisfy ${\mathit{E}}^2$=± √${\mathbf{p}}^2$+${\mathit{m}}^2$. This motivates a proposal to build the phenomenology without explicit reference to a wave equation. We demonstrate the practicality of this approach by providing techniques for constructing the covariant spinors, free-particle field operators, and propagators which could then be used to construct a covariant perturbation theory.