Charges in light cones and quenched infrared radiation

Abstract

The creation of electrically charged states and the resulting electromagnetic fields are considered in spacetime regions in which such experiments can actually be carried out, namely in future-directed light cones. Under the simplifying assumption of external charges, charged states are formed from neutral pairs of opposite charges, with one charge being shifted to light-like infinity. It thereby escapes observation. Despite the fact that this charge moves asymptotically at the speed of light, the resulting electromagnetic field has a well-defined energy operator that is bounded from below. Moreover, due to the spatiotemporal restrictions, the transverse electromagnetic field (the radiation) has no infrared singularities in the light cone. They are quenched and the observed radiation can be described by states in the Fock space of photons. The longitudinal field between the charges (giving rise to Gauss’s law) disappears for inertial observers in an instant. This is consistent with the fact that the underlying longitudinal photons do not manifest themselves as genuine particles. The results show that the restrictions of operations and observations to light cones, which are dictated by the arrow of time, amount to a Lorentz-invariant infrared cutoff.