and magnetic field having the same amplitude and being perpendicular to each other, from the early works of Ritus and Narozhny [@Ritus_1970; @Ritus_1972; @Narozhny_1979; @Narozhny_1980; @Morozov_1981] to the more recent one [@Mironov_2020] (see also Ref. [@Akhmedov_1983] and the reviews in Refs. [@Akhmedov_2011; @Fedotov_2017]), where higher-loop Feynman diagrams have been evaluated. However, so far, in the case of a general plane wave with an arbitrary polarization and shape, only the one-loop mass operator (see Fig. \[FD\_MO\]) and the one-loop polarization operator (see Fig. \[FD\_PO\]) have been computed in Ref. [@Baier_1976_a] and in Refs. [@Becker_1975; @Baier_1976_b], respectively (see also Ref. [@Meuren_2013] for an alternative derivation of the polarization operator).

![The one-loop mass operator in an intense plane wave. The double lines represent exact electron states and propagator in a plane wave (Volkov states and propagator, respectively) [@Landau_b_4_1982].[]{data-label="FD_MO"}](Figure_1.pdf){width="0.6\columnwidth"}

![The one-loop polarization operator in an intense plane wave. The double lines represent exact electron propagators in a plane wave (Volkov propagators) [@Landau_b_4_1982].[]{data-label="FD_PO"}](Figure_2.pdf){width="0.6\columnwidth"}

The one-loop vertex correction in a general plane wave (see Fig. \[FD\_VC\]) has never been evaluated, whereas the corresponding quantity in a constant crossed field was computed in Ref. [@Morozov_1981].

![The one-loop Feynman diagram corresponding to the vertex correction. The double lines 