Calculation of the Resummed Radiation Reaction to Order 1/M Using Heavy Fermion Effective Theory

Abstract

The Abraham-Lorentz-Dirac equation, which is the widely-accepted expression for the recoil force experienced by a radiating charge (known as the \textit{radiation reaction}), displays strange, unphysical behavior. As such, it has been rife with controversy and confusion for over a century. For most of that time, these issues were treated mostly as curiosities and left to the musings of theoreticians. But the advent of high-intensity pulsed tabletop lasers in recent decades has made the radiation reaction relevant to modern experimental physics, which has led to a resurgence of research into the topic. In this dissertation, we calculate the radiation reaction to order $m^{-1}$ experienced by a charge of mass $m$ in an external electromagnetic field resulting from emission of a single photon. To accomplish this, we use heavy fermion effective theory (HFET), which is an effective field theory of QED, and model the total electromagnetic field as the superposition of a quantized self-field associated with the charge and a classical external field. HFET is a novel approach that greatly simplifies the calculation compared to full QED. The simplified calculations allow us to resum our force expression to all orders in $e A_{\text{cl}}$, where $A_{\text{cl}}$ is the background field; this is a novel result. Wilson lines arise in our expressions as a result of resummation.