Canonical approach to photon pressure

Abstract

A theory of radiation pressure and its effects on the gross motion of an aggregrate of charges is established within a canonical framework. The theory indicates the existence of radiation-pressure effects arising from an additional interaction--the R\"ontgen interaction--whose origin is the classical R\"ontgen current. A careful development of the formalism reveals the importance of distinguishing between the canonical and mechanical momenta of the gross motion of the aggregate and of incorporating the R\"ontgen-type interaction terms when calculating the gross-motion dynamics. A form of the R\"ontgen interaction is present even in the dipole approximation: an effect which has previously been ignored but which is necessary to ensure gauge invariance of the radiation-induced mechanical force. Explicit calculations of the rates of change of canonical and mechanical momenta are presented for a general atomic dipole, with specializations to a two-level atom, revealing the presence of velocity-dependent terms in a natural way. The formalism is consistent with the Minkowski form of the classical momentum density of an electromagnetic field.