Operator-valued Feynman integral via conditional Feynman integrals on a function space

Dong Cho

Open Mathematics, Tome 8 (2010), p. 908-927 / Harvested from The Polish Digital Mathematics Library

Résumé

Let C 0r [0; t] denote the analogue of the r-dimensional Wiener space, define X t: C r[0; t] → ℝ2r by X t (x) = (x(0); x(t)). In this paper, we introduce a simple formula for the conditional expectations with the conditioning function X t. Using this formula, we evaluate the conditional analytic Feynman integral for the functional Γtx=exp∫0tθs,xsdηsϕxtx∈Cr0,t , where η is a complex Borel measure on [0, t], and θ(s, ·) and φ are the Fourier-Stieltjes transforms of the complex Borel measures on ℝr. We then introduce an integral transform as an analytic operator-valued Feynman integral over C r [0, t], and evaluate the integral transform for the function Γt via the conditional analytic Feynman integral as a kernel.

Détail

Publié le : 2010-01-01

Zbl 1217.28025

EUDML-ID : urn:eudml:doc:269685

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