Sk. Srinivasan et Ecg. Sudarshan, COMPLEX MEASURES AND AMPLITUDES, GENERALIZED STOCHASTIC-PROCESSES ANDTHEIR APPLICATIONS TO QUANTUM-MECHANICS, Journal of physics. A, mathematical and general, 27(2), 1994, pp. 517-537
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.