On "the plasma approximation"

TL;DR

This paper critiques the plasma approximation in physics, highlighting its inconsistencies and advocating for a proper gauge-invariant approach to accurately describe plasma phenomena.

Contribution

It exposes the fallacy of the plasma approximation and clarifies the correct application of Gauss' law in plasma physics.

Findings

The plasma approximation breaks gauge invariance.

Replacing field equations with Bianchi identities is invalid.

Proper gauge-invariant treatment resolves inconsistencies.

Abstract

``The plasma approximation'' is, in the words of Pauli, ``not even wrong,'' as it expresses a disbelief in the symmetries of the underlying gauge field theory. The electrostatic field in question is divergenceful yet has no sources or sinks, thus breaking Lorentz covariance explicitly, and has no place in a self-consistent theory. Utilizing it leads to inconsistencies in the equation of motion and prevents a proper, field-theoretic treatment of condensed matter in the plasma state. By exposing the fallacy of replacing one of the field equations with one of the Bianchi identities, the applicability of Gauss' law to plasma physics is assured.