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

Kun Soo Chang; Dong Hyun Cho; Il Yoo

Czechoslovak Mathematical Journal (2004)

  • Volume: 54, Issue: 1, page 161-180
  • ISSN: 0011-4642

Abstract

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In this paper, we introduce a simple formula for conditional Wiener integrals over C 0 ( 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 ( 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 ∫ 0 T θ ( s , x ( s ) ) d η ( s ) which are of interest in Feynman integration theories and quantum mechanics.

How to cite

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Chang, Kun Soo, Cho, Dong Hyun, and Yoo, Il. "Evaluation formulas for a conditional Feynman integral over Wiener paths in abstract Wiener space." Czechoslovak Mathematical Journal 54.1 (2004): 161-180. <http://eudml.org/doc/30846>.

@article{Chang2004,
abstract = {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.},
author = {Chang, Kun Soo, Cho, Dong Hyun, Yoo, Il},
journal = {Czechoslovak Mathematical Journal},
keywords = {Banach algebra $S_\{\mathbb \{B\}\}^\{\prime \prime \}$; Banach space $S_\{n, \mathbb \{B\}\}^\{\prime \prime \}$; conditional Wiener integral; conditional Feynman integral; simple formula for conditional Wiener integrals; Banach algebra; conditional Wiener integral; conditional Feynman integral},
language = {eng},
number = {1},
pages = {161-180},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Evaluation formulas for a conditional Feynman integral over Wiener paths in abstract Wiener space},
url = {http://eudml.org/doc/30846},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Chang, Kun Soo
AU - Cho, Dong Hyun
AU - Yoo, Il
TI - Evaluation formulas for a conditional Feynman integral over Wiener paths in abstract Wiener space
JO - Czechoslovak Mathematical Journal
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 1
SP - 161
EP - 180
AB - 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.
LA - eng
KW - Banach algebra $S_{\mathbb {B}}^{\prime \prime }$; Banach space $S_{n, \mathbb {B}}^{\prime \prime }$; conditional Wiener integral; conditional Feynman integral; simple formula for conditional Wiener integrals; Banach algebra; conditional Wiener integral; conditional Feynman integral
UR - http://eudml.org/doc/30846
ER -

References

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