Particle Probes

Abstract

The fermionic fields Ψ and Ψ̄ of QED do not satisfy the conditions that are assumed in the derivation of the LSZ asymptotic conditions. Therefore the experimentally observed electrons and positrons are not particles in the sense of the LSZ formalism, they are expected to be “infraparticles” in the sense of Schroer [Sc 63]. Characteristic for them is a mass-shell singularity in the 2-point functions of their fields which is weaker than the δ-singularity of an ordinary particle. Typically, an infraparticle singularity is of the branch point type θ(p ² - m ²) (p ² - m ²)^-1+α with m the observed mass of the particle and a a small positive number. As a consequence of this weak singularity there exists no 1-particle subspace of the state space, which is an eigenspace of the mass operator M ² = P _µ P ^µ. But the spectrum of M2 still shows a strong concentration near the mass shell: loosely speaking, the density of states is large there. This fact might be used as a starting point for the search of a scattering formalism for infraparticles, by looking for a generalization of the LSZ formalism which is capable of handling this situation. As it turns out, it is more promising to apply a different strategy which is closer to experiment. In this approach a particle is not characterized by possessing a sharp mass but by its spatial localization. This notion of particles describes an observed lumpiness of quantum reality which becomes apparent at low matter densities.