Quasiclassical representation of the Volkov propagator and the tadpole diagram in a plane wave

TL;DR

This paper introduces a fully quasiclassical form of the Volkov propagator in strong-field QED, simplifying calculations by depending only on gauge-invariant quantities and demonstrating that the tadpole diagram vanishes after renormalization.

Contribution

It derives a new quasiclassical expression for the Volkov propagator that simplifies probability calculations and reveals gauge-invariant features in strong-field QED.

Findings

The quasiclassical Volkov propagator depends only on the electron's kinetic four-momentum.

Probabilities can be computed using 2x2 matrices instead of 4x4 matrices.

The tadpole diagram vanishes after renormalization.

Abstract

The solution of the Dirac equation in the presence of an arbitrary plane wave, corresponding to the so-called Volkov states, has provided an enormous insight in strong-field QED. In [Phys. Rev. A \textbf{103}, 076011 (2021)] a new "fully quasiclassical" representation of the Volkov states has been found, which is equivalent to the one known in the literature but which more transparently shows the quasiclassical nature of the quantum dynamics of an electron in a plane-wave field. Here, we derive the corresponding expression of the propagator by constructing it using the fully quasiclassical form of the Volkov states. The found expression allows one, together with the fully quasiclassical expression of the Volkov states, to compute probabilities in strong-field QED in an intense plane wave by manipulating only 2-by-2 rather than 4-by-4 Dirac matrices as in the usual approach. Moreover, apart from the exponential functions featuring the classical action of an electron in a plane wave, the fully quasiclassical Volkov propagator depends only on the electron kinetic four-momentum in the plane wave, which is a gauge-invariant quantity. Finally, we also compute the one-loop tadpole diagram in a plane wave starting from the Volkov propagator and we find that after renormalization it identically vanishes.