Radiation in (2+1)-dimensions

Abstract

In this paper we discuss the radiation equation of state p = ρ/2 in (2+1)-dimensions. In (3+1)dimensions the equation of state p = ρ/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 = ρ/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 = 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.