Charges in light cones and quenched infrared radiation
Detlev Buchholz, Fabio Ciolli, Giuseppe Ruzzi, Ezio Vasselli
TL;DR
The paper addresses infrared issues in QED by restricting measurements to future-directed light cones $V_+$. It develops an algebraic framework with Gupta–Bleuler fields and extended gauge variables to construct charged states via bi-localized charges and shifting compensating charges to light-like infinity, ensuring energy boundedness and unitary implementability of translations with the relativistic spectrum condition. The key results show that infrared radiation in $V_+$ is describable in the photon Fock space, infrared clouds are quenched, and longitudinal gauge-bridges become observationally inaccessible within inertial frames, effectively providing a Lorentz-invariant infrared cutoff. Collectively, these findings imply that restricting operations to light cones removes the traditional infrared problems of Minkowski-space QED and clarifies the physical status of gauge bridges and longitudinal photons.
Abstract
The creation of electrically charged states and the resulting electromagnetic fields are considered in space-time 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 there is no evidence for the existence of longitudinal photons. 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.