On Feynman's proof of the Maxwell equations

Feynman's proof, as recounted by F. J. Dyson [Am. J. Phys. 58, 209--211 (1990)], that the Lorentz force law and two of Maxwell's equations can apparently be deduced from minimal assumptions about the equation of motion and quantization condition for a nonrelativistic particle, is analyzed. A version of this result is found to hold in classical mechanics, and it is shown that instead of limiting interactions to electromagnetic ones, Feynman's result is a rederivation of the constraints on the velocity-dependent generalized forces that can be accommodated in a canonical Lagrangian formalism. The generality of the result is illustrated by showing that particle motion in a noninertial frame or in a weak gravitational field also satisfies the constraints