  Physical path integral formulation of motion of particles in Riemannian
spaces is outlined and extended to deduce the corresponding field theoretical
formulation. For the special case of a zero rest mass particle in Minkowski
manifold, it is shown that the underlying space can be reduced to
three-dimensional while similar formulation for a massive particle requires a
four-dimensional structure. The solutions obtained by the present procedure are
compared with the results obtained from its counterpart for a massive particle
by setting the mass equal to zero. Although similar, the present formulation
has some additional implications pertaining to the energy spectrum and the
associated free field quantization, particularly it yields zero vacuum energy.
The results are naturally extended to higher dimensions.
