Covariance, Curved Space, Motion and Quantization

Weak external forces and non-inertial motion are equivalent with the free motion in a curved space. The Hamilton-Jacobi equation is derived for such motion and the effects of the curvature upon the quantization are analyzed, starting from a generalization of the Klein-Gordon equation in curved spaces. It is shown that the quantization is actually destroyed, in general, by a non-inertial motion in the presence of external forces, in the sense that such a motion may produce quantum transitions. Examples are given for a massive scalar field and for photons. Newton’s law. We start with Newton’s law m dv dt = f; (1) for a particle of massm, with usual notations. I wish to show here that it is equivalent with the motion of a free particle of massm in a curved space, i.e. it is equivalent wit