Physical Review · 1948 · 281 citations · 4 references
Natural SciencesPhysicsElectromagnetismQuantum MechanicsTheoretical PhysicsAccelerator PhysicsRelativistic ElectrodynamicsRelativistic PhysicsRelativistic Quantum MechanicsStrong InteractionWave-particle InteractionsLight ConesPair Production
Ordinarily it is assumed that interaction between charges occurs along light cones, that is, only where the four‑dimensional interval \(s^{2}=t^{2}-r^{2}\) is exactly zero. The study investigates the effects of assuming substantial interaction over a narrow range of \(s^{2}\) around zero, as proposed by F. Bopp. The authors analyze these modifications by considering a finite interaction range around the light cone.
Ordinarily it is assumed that interaction between charges occurs along light cones, that is, only where the four-dimensional interval ${s}^{2}={t}^{2}\ensuremath{-}{r}^{2}$ is exactly zero. We discuss the modifications produced if, as in the theory of F. Bopp, substantial interaction is assumed to occur over a narrow range of ${s}^{2}$ around zero. This has no practical effect on the interaction of charges which are distant from one another by several electron radii. The action of a charge on itself is finite and behaves as electromagnetic mass for accelerations which are not excessive. There also results a classical representation of the phenomena of pair production in sufficiently strong fields.
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