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A complex scaling approach to sequential Feynman integrals

Author

Listed:
  • Luo, S. L.
  • Yan, J. A.

Abstract

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] >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.

Suggested Citation

  • Luo, S. L. & Yan, J. A., 1999. "A complex scaling approach to sequential Feynman integrals," Stochastic Processes and their Applications, Elsevier, vol. 79(2), pages 287-300, February.
    • Handle: RePEc:eee:spapps:v:79:y:1999:i:2:p:287-300
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    References listed on IDEAS

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    1. Yan, Jia-An, 1994. "From Feynman-Kac formula to Feynman integrals via analytic continuation," Stochastic Processes and their Applications, Elsevier, vol. 54(2), pages 215-232, December.
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