Radiation in (2+1)(2+1)-dimensions

In this paper we discuss the radiation equation of state p=ρ/2p=ρ/2 in (2+1)(2+1)-dimensions. In (3+1)(3+1)-dimensions the equation of state p=ρ/3p=ρ/3 may be used to describe either actual electromagnetic radiation (photons) or 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)(2+1)-dimensional Maxwell electrodynamics the radiation law p=ρ/2p=ρ/2 takes place only for plane waves, i.e. for E=BE=B. Instead of the linear Maxwell electrodynamics, to derive the (2+1)(2+1)-radiation law for more general cases with E≠BE≠B, one has to use a conformally invariant electrodynamics, which is a (2+1)(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.