  Analysis of the original Feynman's formula for a moving point charge leads to
the notion of a retarded time, which has to be treated as a field.
  The Lorentzian frame, the trajectory, and the retarded time field uniquely
determine a system of fields over the frame, which the author calls the
fundamental fields.
  By means of these fields one can represent and establish relations between
the wave, Lorentz gauge, and Maxwell equations, and to prove that
electromagnetic field generated by Lienard-Wiechert potentials, and the fields
represented by the amended Feynman's formula coincide, and both fields satisfy
Maxwell equations and homogenous wave equations.
  One of the main results is contained in Bogdan-Feynman Theorem for a moving
point mass combining all important aspects of the development into a single
mathematical theorem.
  This theorem leads, for instance, to a field generated by a point mass, that
in its rest frame represents Newton's gravity field, if neglecting the constant
of proportionality.
  The rest of the paper is devoted to the study of n-body problems for various
general relativistic force fields and to prove the existence and uniqueness of
solutions. Such problems lead to nonanticipating differential equations,
solutions of which depend not only on the initial data, but also on the initial
trajectory of the entire system of bodies.
  To analyze such equations author develops a theory of nonanticipating
uniformly Lipschitzian operators on trajectories of such systems.
