Charge density and electric charge in quantum electrodynamics

Abstract

The convergence of integrals over charge densities is discussed in relation with the problem of electric charge and (nonlocal) charged states in quantum electrodynamics. Delicate points like the domain dependence of local charges as quadratic forms and the class of time smearing ensuring strong convergence of integrals of charge densities are analyzed and shown to be crucial in QED, also for the control of vacuum polarization effects leading to time dependence of the charge (Swieca phenomenon). The possibility of constructing physical charged states in the Feynman–Gupta–Bleuler gauge as limits of local state vectors is discussed, compatibly with the vanishing of the Gauss charge on local states. A modification of the Dirac exponential factor which yields the physical Coulomb fields from the Feynman–Gupta–Bleuler fields is shown to remove the infrared divergence of scalar products of local and physical charged states, allowing for a construction of physical charged fields with well-defined correlation functions with local fields.