Effective action approach to wave propagation in scalar QED plasmas

TL;DR

This paper develops a relativistic quantum field theory approach to wave propagation in scalar QED plasmas, deriving gauge-invariant effective actions that reveal quantum modifications to classical plasma wave behavior.

Contribution

It introduces a novel effective action framework for scalar QED plasmas, enabling analysis of quantum effects on plasma wave dispersion relations.

Findings

Classical plasma waves are recovered in the classical limit.

Quantum effects modify wave dispersion relations significantly.

New wave phenomena like nonzero group velocity and persistent Bernstein waves are identified.

Abstract

A relativistic quantum field theory with nontrivial background fields is developed and applied to study waves in plasmas. The effective action of the electromagnetic 4-potential is calculated ab initio from the standard action of scalar QED using path integrals. The resultant effective action is gauge invariant and contains nonlocal interactions, from which gauge bosons acquire masses without breaking the local gauge symmetry. To demonstrate how the general theory can be applied, we study a cold unmagnetized plasma and a cold uniformly magnetized plasma. Using these two examples, we show that all linear waves well-known in classical plasma physics can be recovered from relativistic quantum results when taking the classical limit. In the opposite limit, classical wave dispersion relations are modified substantially. In unmagnetized plasmas, longitudinal waves propagate with nonzero group velocities even when plasmas are cold. In magnetized plasmas, anharmonically spaced Bernstein waves persist even when plasmas are cold. These waves account for cyclotron absorption features observed in spectra of X-ray pulsars. Moreover, cutoff frequencies of the two non-degenerate electromagnetic waves are redshifted by different amounts. These corrections need to be taken into account in order to correctly interpret diagnostic results in laser plasma experiments.