Classical electrodynamics with vacuum polarization: electron self-energy and radiation reaction

Abstract

The region very close to an electron ( r ⪅ r 0 = e 2/ mc 2 ≈ 2.8 × 10 −13 cm) is, according to quantum electrodynamics, a seething maelstrom of virtual electron-positron pairs flashing in and out of existence. To take account of this well-established physical reality, a phenomenological representation for vacuum polarization is introduced into the framework of classical electrodynamics. Such a model enables a consistent picture of classical point charges with finite electromagnetic self-energy. It is further conjectured that the reaction of a point charge to its own electromagnetic field is tantamount to interaction with its vacuum polarization charge or “aura.” This leads to a modification of the Lorentz-Dirac equation for the force on an accelerating electron, a new differential-difference equation which avoids the pathologies of preacceleration and runaway solutions.