Radiation in (2+1)-dimensions

TL;DR

This paper explores the radiation equation of state in (2+1)-dimensional electrodynamics, showing that the linear Maxwell theory yields a specific law only for plane waves, while more general cases require nonlinear, conformally invariant theories.

Contribution

It demonstrates that in (2+1)-dimensions, the radiation law p=ρ/2 applies only to plane waves within Maxwell theory, and proposes using nonlinear conformally invariant electrodynamics for more general cases.

Findings

The radiation law p=ρ/2 applies only to plane waves with E=B.

Nonlinear conformally invariant electrodynamics is needed for general E ≠ B cases.

A volumetric average of the stress-energy tensor yields the radiation law in (2+1) dimensions.

Abstract

In this paper we discuss the radiation equation of state $p=\rho/2$ in (2+1)-dimensions. In (3+1)-dimensions the equation of state $p=\rho/3$ may be used to describe either actual electromagnetic radiation (photons) as well as a gas of massless particles in a thermodynamic equilibrium (for example neutrinos). In this work it is shown that in the framework of (2+1)-dimensional Maxwell electrodynamics the radiation law $p=\rho/2$ takes place only for plane waves, i.e. for $E = B$. Instead of the linear Maxwell electrodynamics, to derive the (2+1)-radiation law for more general cases with $E \neq B$, one has to use a conformally invariant electrodynamics, which is a 2+1-nonlinear electrodynamics with a trace free energy-momentum tensor, and to perform a volumetric spatial average of the corresponding Maxwell stress-energy tensor with its electric and magnetic components at a given instant of time $t$.