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Fourier-Feynman transforms and the first variation. (English) Zbl 0907.28008

Summary: In this paper we complete the following four objectives: 1. We obtain an integration by parts formula for analytic Feynman integrals. 2. We obtain an integration by parts formula for Fourier-Feynman transforms. 3. We find the Fourier-Feynman transform of a functional \(F\) from a Banach algebra \({\mathcal S}\) after it has been multiplied by \(n\) linear factors. 4. We evaluate the analytic Feyman integral of functionals like those described in 3 above. A very fundamental result by R. H. Cameron and D. A. Storvick [Gaussian random fields, Singapore: World Scientific, Ser. Probab. Stat. 1, 144-157 (1991; Zbl 0820.46045)], Theorem 1], in which they express the analytic Feynman integral of the first variation of a functional \(F\) in terms of the analytic Feynman integral of \(F\) multiplied by a linear factor, plays a key role throughout this paper.

MSC:

28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
46G12 Measures and integration on abstract linear spaces
81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic geometry

Citations:

Zbl 0820.46045
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Full Text: DOI

References:

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