COMPLEX MEASURES AND AMPLITUDES, GENERALIZED STOCHASTIC-PROCESSES ANDTHEIR APPLICATIONS TO QUANTUM-MECHANICS

Complex measure theory is used to widen the scape of the study of stoc hastic processes and it is shown how, with such an extension, the phys ical concepts of superposition and diffraction follow automatically. T he Dirac-Feynman path integral formalism is seen as a natural developm ent. Several generic Markov processes are studied when extended to com plex measures. The role of conditional expectations in this framework as propagating amplitudes is brought out with special reference to the Huyghens' princple. Diffusion is studied in this extended formalism a nd the context in which the Schrodinger or Dirac equation can be deriv ed is stated. The Hamiltonian evolution and decay of correlations requ ire complex measures which are boundary values of analytic functions.