Nonperturbative approach to the infrared behavior in physical charged sectors of gauge theories

Physical charged fields in Abelian gauge theories with unbroken global gauge symmetry are constructed. The Bloch-Nordsieck approximation is then used for the investigation of their mass-shell behavior in both cases of unconfined and confined global charge. In the former case (we consider spinor QED) physical charged fields are found to have vanishing infrared anomalous dimension and to admit the conventional Lehmann-Symanzik-Zimmermann (LSZ) limit. In the latter case (we consider a toy model obtained from QED by replacing the photon with a dipole gluon) it turns out that physical charged fields have zero LSZ limit and the relative Green's functions exhibit an essential singularity in the coupling constant $g$ at $g=0\mathrm{}$. Moreover, the perturbative expansion of these Green's functions, although asymptotic, is not Borel summable.