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Volkov states and Volkov propagator are the basic analytical tools toinvestigate QED processes occurring in the presence of an intense plane-waveelectromagnetic field. In the present paper we provide alternative andrelatively simple proofs of the completeness and of the orthonormality at afixed time of the Volkov states. Concerning the completeness, we exploit someknown properties of the Green's function of the Dirac operator in a plane wave,whereas the orthonormality of the Volkov states is proved, relying only on ageometric argument based on the Gauss theorem in four dimensions. In relationwith the completeness of the Volkov states, we also study some analyticalproperties of the Green's function of the Dirac operator in a plane wave, whichwe explicitly prove to coincide with the Volkov propagator in configurationspace. In particular, a closed-form expression in terms of modified Besselfunctions and Hankel functions is derived by means of the operator technique ina plane wave and different asymptotic forms are determined. Finally, thetransformation properties of the Volkov propagator under general gaugetransformations and a general gauge-invariant expression of the so-calleddressed mass in configuration space are presented.

On the completeness and orthonormality of the Volkov states and the Volkov propagator in configuration space