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We argue that the theories of Volokitin and Persson (2014 New J. Phys. 16 118001), Dedkov and Kyasov (2008 J. Phys.: Condens. Matter 20 354006), and Pieplow and Henkel (2013 New J. Phys. 15 023027) agree on the electromagnetic force on a small, polarizable particle that is moving parallel to a planar, macroscopic body, as far as the contribution of evanescent waves is concerned. The apparent differences are discussed in detail and explained by choices of units and integral transformations. We point out in particular the role of the Lorentz contraction in the procedure used by Volokitin and Persson, where a macroscopic body is 'diluted' to obtain the force on a small particle. Differences that appear in the contribution of propagating photons are briefly mentioned.
The electromagnetic force on a polarizable particle is calculated in a covariant framework. Local equilibrium temperatures for the electromagnetic field and the particle's dipole moment are assumed, using a relativistic formulation of the fluctuation-dissipation theorem. Two examples illustrate radiative friction forces: a particle moving through a homogeneous radiation background and above a planar interface. Previous results for arbitrary relative velocities are recovered in a compact way.