  We describe different approximations associated with employing a constant
matrix element for the coupling of light to multiband electrons in the context
of time-resolved angle-resolved photoemission spectroscopy (TR-ARPES). In
particular, we demonstrate that the constant matrix approximation only holds
for one of the coordinate representations, and changing to other bases,
requires including nonconstant corrections to the matrix element. We also
discuss some simplifying approximations, where a constant matrix element is
employed in multiple bases, and the consequences of this further approximation
(especially with respect to the TR-ARPES signal no longer being nonnegative).
We also discuss issues related to gauge invariance of the final spectra.
