Abstract

Distributions on abstract Wiener spaces are constructed via the second quantization of a basic self adjoint operator on the Cameron-Martin-Maruyama space. Using properties of Hilbert space traces, a rigorous construction of the Feynman integral is given as a distribution on a suitable space of test functions. A martingale approximation to the Feynman distribution is also derived. A new result on the characterization of positive distributions is obtained and is applied to an example of interest in Quantum Field theory.

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