Sideband mixing in intense laser backgrounds

The electron propagator in a laser background has been shown to be made up of a series of sideband poles. In this paper we study this decomposition by analysing the impact on the sidebands of the residual gauge freedom in the Volkov solution. We show that these gauge transformations do not alter the location of the poles although the wave function renormalisation is gauge dependent. Our identification of the propagator from the diagonal part of the two-point function in the laser background is maintained but we show that the sideband structures mix under residual gauge transformations