Path integral formulation of quantized fields

Abstract

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.