A complex scaling approach to sequential Feynman integrals

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:79

Article

Luo, SL ; Yan, JA

关键词: analytic Feynman integrals;    Cameron-Martin-type formula;    complex scaling;    Feynman-Wiener integrals;    Fresnel integrals;    sequential Feynman integrals;    trace;   

DOI  :  10.1016/S0304-4149(98)00076-3

来源: Elsevier

【 摘 要 】

Let (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.

【 授权许可】

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