Abstract
Exploiting the gauge freedom associated with the Volkov description of a charge propagating in a plane wave background, we identify a new type of gauge choice which significantly simplifies the theory. This allows us to develop a compact description of the propagator for both scalar and fermionic matter, in a circularly polarised background. It is shown that many of the usually observed structures are gauge artefacts. We then analyse the full ultraviolet behaviour of the one-loop corrections for such charges. This enables us to identify and contrast the different renormalisation prescriptions needed for both types of matter.
Highlights
Very early in the development of quantum electrodynamics, QED, it was understood that the interaction of light with matter was best described in a way that introduced extra, unphysical, degrees of freedom [1,2]
The Volkov solution has built into it a gauge freedom
In this paper we have introduced an additional gauge fixing condition on the background, which we call the momentum gauge, which dramatically simplifies the description of charged matter propagation
Summary
Very early in the development of quantum electrodynamics, QED, it was understood that the interaction of light with matter was best described in a way that introduced extra, unphysical, degrees of freedom [1,2]. We shall see that this holds for both weak and strong backgrounds, and leads to clear renormalization conditions on the fields and physical parameters This will be shown for both scalar and fermionic matter, and in this way we will be able to highlight and contrast some of the simple results found here for the renormalization of both theories through the use of our additional gauge fixing condition on the background. We will be able to explicitly introduce counterterms and renormalize using standard field theory constructions That this can be done for both types of matter and for both weak and strong backgrounds, points to the great utility of imposing our additional gauge fixing condition on the background.
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