Abstract
Part I of this paper shows that by using a probability measure on the space of Feynman's path integrals, together with the notion of “Hermitian functionals” it is possible to express Feynman's results in a mathematically less obscure form. Part II is concerned with physical interpretation, involving a continuation of the configuration variable into the imaginary direction, together with the recognition of a hydrodynamical analogy. Part III employs these ideas to give a new general proof of the equivalence of Feynman's integral and the solution of Schrodinger's equation. Part IV discusses interesting properties of certain paths in the complex plane.
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