Evaluation formulas for a conditional Feynman integral over Wiener paths in abstract Wiener space

Title:

Evaluation formulas for a conditional Feynman integral over Wiener paths in abstract Wiener space

Creator:

Chang, Kun Soo, Cho, Dong Hyun, and Yoo, Il

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:e1d3439b-6a05-4cf2-bcf9-8c3bd064b282
uuid:e1d3439b-6a05-4cf2-bcf9-8c3bd064b282

Subject:

Banach algebra $S_{\mathbb{B}}^{\prime \prime }$, Banach space $S_{n, \mathbb{B}}^{\prime \prime }$, conditional Wiener integral, conditional Feynman integral, and simple formula for conditional Wiener integrals

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

In this paper, we introduce a simple formula for conditional Wiener integrals over $C_0(\mathbb{B})$, the space of abstract Wiener space valued continuous functions. Using this formula, we establish various formulas for a conditional Wiener integral and a conditional Feynman integral of functionals on $C_0(\mathbb{B})$ in certain classes which correspond to the classes of functionals on the classical Wiener space introduced by Cameron and Storvick. We also evaluate the conditional Wiener integral and conditional Feynman integral for functionals of the form \[ \exp \biggl \lbrace \int _0^T \theta (s, x(s))\mathrm{d}\eta (s) \biggr \rbrace \] which are of interest in Feynman integration theories and quantum mechanics.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

161-180

Source:

Czechoslovak Mathematical Journal | 2004 Volume:54 | Number:1

Harvested from:

CDK

Metadata only:

false