PARTICLE MOTION AND INTERACTION IN NONLINEAR FIELD THEORIES

A variational method is given for determining the motion and interaction of particles associated with fields governed by nonlinear differential equations. For field equations derived from Lagrangian densities of the type g ικ(∂θ/∂xι)(∂θ/ ∂xκ) + f(θ), one obtains an attractive inverse-square law of force between like particles, provided f(θ) vanishes more rapidly than (constant) θ4 for θ → 0.