Power corrections to the HTL effective Lagrangian of QED

TL;DR

This paper derives compact expressions for power corrections to the HTL Lagrangian of QED in various dimensions, addressing divergence regularization and potential generalizations to dense media.

Contribution

It provides the first compact, gauge-invariant expressions for order $(L/T)^2$ corrections to the HTL Lagrangian in QED across different dimensions.

Findings

Regularized divergences in the HTL Lagrangian using dimensional regularization.

Achieved gauge-invariant power corrections valid for momenta much less than temperature.

Discussed extensions to include chemical potential for dense plasma conditions.

Abstract

We present compact expressions for the power corrections to the hard thermal loop (HTL) Lagrangian of QED in $d$ space dimensions. These are corrections of order $(L/T)^2$, valid for momenta $L \ll T$, where $T$ is the temperature. In the limit $d\to 3$ we achieve a consistent regularization of both infrared and ultraviolet divergences, which respects the gauge symmetry of the theory. Dimensional regularization also allows us to witness subtle cancellations of infrared divergences. We also discuss how to generalise our results in the presence of a chemical potential, so as to obtain the power corrections to the hard dense loop (HDL) Lagrangian.