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A complex scaling approach to sequential Feynman integrals
Luo, SL; Yan, JA
AbstractLet (H, B, mu) be an abstract Wiener space. Let P be the set of all finite-dimensional orthogonal projections in H and for P is an element of P denote by Gamma(P) the second quantization of P. It is shown that for phi is an element of boolean AND(p>1) L-p(B, mu) and z is an element of C+ = {z is an element of C: Re z > 0}, 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(P-n)phi, 1]] if the latter exists and has a common limit for all z(n) --> i, z(n) is an element of C+, P-n --> I, P-n is an element of P. 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. (C) 1999 Elsevier Science B.V. All rights reserved.
Keywordanalytic Feynman integrals Cameron-Martin-type formula complex scaling Feynman-Wiener integrals Fresnel integrals sequential Feynman integrals trace
WOS Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000078561000007
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Document Type期刊论文
Corresponding AuthorLuo, SL
AffiliationAcad Sinica, Inst Appl Math, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Luo, SL,Yan, JA. A complex scaling approach to sequential Feynman integrals[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS,1999,79(2):287-300.
APA Luo, SL,&Yan, JA.(1999).A complex scaling approach to sequential Feynman integrals.STOCHASTIC PROCESSES AND THEIR APPLICATIONS,79(2),287-300.
MLA Luo, SL,et al."A complex scaling approach to sequential Feynman integrals".STOCHASTIC PROCESSES AND THEIR APPLICATIONS 79.2(1999):287-300.
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