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) [circle plus] (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) [circle plus] (0,1), (3/2,0) [circle plus] (0,3/2) and (2,0) [circle plus] (0,2) matter fields. The m [to] 0 limit of the covariant spinors is shown to have the expected structure. The algebra of the [gamma][^uv] matrices associated with the (1, 0) [circle plus] (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 [greater than or equal to] 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) [circle plus] (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) [circle plus] (0,1) and (3/2,0) [circle plus] (0,3/2) matter fields, and the same conclusions obtained. A well-known set of linear equations for massless free particles of arbitrary spin is found to have acausal solutions. On the other hand, the m [to] 0 limit of the wave equations satisfied by ( j ,0) [circle plus] (0, j ) covariant spinors are free from all kinematical acausality. This paradoxical situation is resolved and corrected through the introduction of a constraining principle. The appendix reviews and presents in a unified framework classic works of Schwinger, Weinberg and Wigner regarding the elements of canonical quantum field theory, thus establishing the logical context of our work.