Quantum field theory and the dynamical role of spin

Abstract

The point of view currently taken in elementary particle physics, that the spin is an unessential complication and plays no dynamical role, is criticized here. This assumption has no experimental ground; it is merely a consequence of the wave equations used, especially in field theory. To get rid of it, we must define wave functions and fields as functions, not on Minkovski space, but on the Poincar\'e manifold (i.e., the manifold of the Poincar\'e group). The result is a ``Poincar\'e field theory," for which the general features of field theory (relativistic invariance, locality, definition of free fields) are formulated. The spectral condition is only sketched. A physically important result is a generalized Kall\`en - Lehmann representation of the two-point function, where the spectral function depends on the mass and also on the spin. As a consequence, the peaks in this spectral function represent particles which may have different spin values, and (when they are unstable) a spin spectrum as well as a mass spectrum. The notion of Regge trajectory appears as a particular case.