Integration by parts formulas for analytic Feynman integrals of unbounded functionals

Abstract

Chang, Choi and Skoug established several integration by parts formulas involving generalized Feynman integrals, generalized Fourier-Feynman transforms, and the first variation of cylinder-type functionals. We establish integration by parts formulas for analytic Feynman integrals of unbounded functionals on abstract Wiener space having the formwhere G belongs to the Fresnel class F (B) and = ψ + φ with ψ ∈ L 1 (R n ) and φ is the Fourier transform of a complex Borel measure of bounded variation on R n . We also study integration by parts formulas for the analytic Feynman integral involving the Fourier-Feynman transform of those functionals in F (B).

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