A complex scaling approach to sequential Feynman integrals

Let (H,B,[mu]) be an abstract Wiener space. Let be the set of all finite-dimensional orthogonal projections in H and for denote by [Gamma](P) the second quantization of P. It is shown that for [phi][set membership, variant][intersection operator]p>1Lp(B,[mu]) and , the z-1/2-scaling [sigma]z-1/2[Gamma](P)[phi] of [Gamma](P)[phi] is well defined as an element of a distribution space over (H,B,[mu]). By means of this scaling, we define the sequential Feynman integral as limn-->[infinity]<<[sigma]zn-1/2[Gamma](Pn)[phi],1>>if the latter exists and has a common limit for all . It turns out that the Fresnel integrals of Albeverio and Hoegh-Krohn coincide with this sequential Feynman integrals. The proof of a Cameron-Martin-type formula for Feynman integrals is much simplified and transparent.