One loop Volkov propagator in the Lorentz class of gauges

Abstract

We calculate the ultraviolet divergences in a weak field expansion of the Volkov propagator. This is done for the full Lorentz class of gauges. The expected gauge invariance of the vacuum mass shift in each sideband is recovered. However, the renormalisation of the background induced mass shift is shown to be gauge dependent. In particular, we show that it vanishes in Landau gauge. We find that only in that gauge does the vacuum renormalisation remove all ultraviolet divergences.

Loop spin effects in intense background fields

“…where g is the electron's gyromagnetic ratio or "g factor". Compare this to the exact evolution equation for (22), which is FIG. 4.…”

“…In Cartesian components, the basis elements used in the BMT calculation, as defined in and below (22), obey…”

“…Using the locally constant field approximation (LCFA) [8], this radiative spin flip has been included in numerical schemes [17][18][19]. However, the spin can also change in a nonradiative way, through quantum loop effects [20][21][22]. (See [23][24][25][26][27][28][29][30], also [31][32][33][34], for investigations of higher loop orders in strong fields, which has recently seen renewed interest.)…”

Simplest description of charge propagation in a strong background

“…The one-loop ultraviolet results ( 25) and ( 28), and the expansion of the double line propagator (18), are the only ingredients needed for building the full, one-loop, ultraviolet corrections to the scalar propagator in the background. This claim might seem surprising as we have only considered a single seagull interaction, but we note that if a loop straddles more than one background interaction, then it is ultraviolet finite by simple power counting.…”

“…Recognising in this expression the double line expansions (18) squared, allows us to write (32) as the double line self-energy:…”