Renormalization of the Volkov propagator

Martin Lavelle,David Mcmullan

doi:10.1103/physrevd.100.036001

Martin Lavelle, David Mcmullan

Open Access

https://doi.org/10.1103/physrevd.100.036001

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Abstract

The perturbative description of an electron propagating in a plane wave background is developed and loop corrections analysed. The ultraviolet divergences and associated renormalisation are studied using the sideband framework within which the multiplicative form of the corrections becomes manifest. An additional renormalisation beyond that usually expected is identified and interpreted as a loop correction to the background induced mass term. Results for the strong field sector are conjectured.

Highlights

The Volkov solution [1] for an electron in a plane wave background is one of the key theoretical building blocks underpinning our understanding of how matter interacts with a laser
Where we have defined the loop correction to the final term in (34): Σ= M. From this we find that the loop corrections to the central sidebands (36) are given by
In this paper we have developed a perturbative description of the propagation of an electron in a plane wave background

Summary

INTRODUCTION

The Volkov solution [1] for an electron in a plane wave background is one of the key theoretical building blocks underpinning our understanding of how matter interacts with a laser. Unitarity arguments are often used to directly link loop corrections to effective cross sections It has been argued, see e.g., [23], that the laser background has no impact on the renormalization of the theory. The incorporation of loops in the weak field limit will follow using standard perturbative methods This will allow us to better understand the way in which loops are added to the double line, see Fig. 2. In this paper we will study the renormalization of the theory describing an electron propagating in a plane wave background This analysis will start in the weak intensity regime and there we will calculate the ultraviolet divergences. Renormalization is most studied within a momentum space description of the theory, so we conclude with a discussion on how a consistent momentum space language can be applied to this system where translation invariance has been broken by the background field, and conjecture all orders results

THE PERTURBATIVE SETUP

HIGHER ORDER BACKGROUND CORRECTIONS

ABSORPTION AND EMISSION FROM THE BACKGROUND

RENORMALIZATION

THE FULL VOLKOV DESCRIPTION AT ONE LOOP

CONCLUSIONS