Formulisms of path integrals in momentum space and in mixed spaces

We define the Lagrangians in the momentum space and in mixed position-momen tum spaces. In terms of the so-defined Lagrangians, the actions and the pro pagators are directly defined in the spaces, not as the Fourier transforms of their counterparts in the configuration space as previously known in the literature. (C) 2000 Elsevier Science B.V. All lights reserved.