RELATIVISTIC GENERALIZATION AND EXTENSION TO THE NON-ABELIAN GAUGE-THEORY OF FEYNMAN PROOF OF THE MAXWELL EQUATIONS

R. P. Feynman showed F. J. Dyson a proof of the Lorentz force law and the homogeneous Maxwell equations, which the obtained starting from Newton's law of motion and the commutation relations between position and velocity for a single nonrelativistic particle. We formulate both a special relativistic and a general relativistic versions of Feynman's derivation. Especially in the general relativistic version we prove that the only possible fields that can consistently act on a quantum mechanical particle are scalar, gauge, and gravitational fields. We also extend Feynman's scheme to the case of non-Abelian gauge theory in the special relativistic context. © 1992 Academic Press, Inc.