Remarks on Tanimura's reformulation of general relativistic version of Feynman's proof about Maxwell equations

Abstract

We reformulate the genaral relativistic version given by S.Tanimura of Feynman's consideration. Velocity and momentum of a point particle are assumed to be transformed as (contravariant and covariant) vectors under the point transformation in quantum mechanical sense. Such an assumption restricts strongly the equation of motion allowed by the basic commutation relations. This equation is equivalent to Hamilton-type one including scalar, vector and gravitational fields covariantly.