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The long-standing resolution of the Abraham--Minkowski electromagneticmomentum controversy is predicated on a decomposition of the total momentum ofa closed continuum electrodynamic system into separate field and mattercomponents. Using a microscopic model of a simple linear dielectric, we deriveLagrangian equations of motion for the electric dipoles and show that thedielectric can be treated as a collection of stationary simple harmonicoscillators that are driven by the electric field and produce a polarizationfield in response. The macroscopic energy and momentum are defined in terms ofthe electric, magnetic, and polarization fields that travel through thedielectric together as a pulse of electromagnetic radiation. We conclude thatboth the macroscopic energy and the macroscopic momentum are entirelyelectromagnetic in nature for a simple linear dielectric in the absence ofsignificant reflections.

Decomposition of the Total Electromagnetic Momentum in a Linear Dielectric into Field and Matter Components