scholarly journals A Cameron-Storvick theorem for the analytic Feynman integral associated with Gaussian paths on a Wiener space and applications

2018 ◽  
Vol 17 (6) ◽  
pp. 2225-2238 ◽  
Author(s):  
Seung Jun Chang ◽  
◽  
Jae Gil Choi
Keyword(s):  
Feynman Integral ◽  
Wiener Space ◽  
Analytic Feynman Integral

scholarly journals Analytic Feynman Integral and a Change of Scale Formula for Wiener Integrals of an Unbounded Cylinder Function

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Kim Young Sik
Keyword(s):  
Feynman Integral ◽  
Wiener Space ◽  
Wiener Integral ◽  
Unbounded Function ◽  
Cylinder Function ◽  
Analytic Feynman Integral ◽  
Change Of Scale ◽  
Unbounded Cylinder

We investigate the behavior of the unbounded cylinder function F x = ∫ 0 T α 1 t d x t 2 k ⋅ ∫ 0 T α 2 t d x t 2 k ⋅ ⋯ ⋅ ∫ 0 T α n t d x t 2 k ,   k = 1,2 , … whose analytic Wiener integral and analytic Feynman integral exist, we prove some relationships among the analytic Wiener integral, the analytic Feynman integral, and the Wiener integral, and we prove a change of scale formula for the Wiener integral about the unbounded function on the Wiener space C 0 0 , T .

scholarly journals A change of scale formula for Wiener integrals of cylinder functions on abstract Wiener space

1998 ◽  
Vol 21 (1) ◽  
pp. 73-78 ◽  
Author(s):  
Young Sik Kim
Keyword(s):  
Feynman Integral ◽  
Wiener Space ◽  
Abstract Wiener Space ◽  
Wiener Integral ◽  
Feynman Integrals ◽  
Analytic Feynman Integral ◽  
Change Of Scale ◽  
The Relationship

The purpose of this paper is to establish the existence of analytic Wiener and Feynman integrals for a class of certain cylinder functions which is of the form:F(x)=f((h1,x)∼,⋯,(hn,x)∼),    x∈B,on the abstract Wiener space, and to establish the relationship between the Wiener integral and the analytic Feynman integral for such cylinder functions on the abstract Wiener space. We then establish a change of scale formula for Wiener integrals of such cylinder functions on the abstract Wiener space.

scholarly journals A change of scale formula for Wiener integrals of cylinder functions on the abstract Wiener space II

2001 ◽  
Vol 25 (4) ◽  
pp. 231-237 ◽  
Author(s):  
Young Sik Kim
Keyword(s):  
Fourier Transform ◽  
Borel Measure ◽  
Feynman Integral ◽  
Wiener Space ◽  
Abstract Wiener Space ◽  
Analytic Feynman Integral ◽  
Change Of Scale ◽  
The Fourier Transform ◽  
Complex Valued

We show that for certain bounded cylinder functions of the formF(x)=μˆ((h1,x)∼,...,(hn,x)∼),x∈Bwhereμˆ:ℝn→ℂis the Fourier-transform of the complex-valued Borel measureμonℬ(ℝn), the Borelσ-algebra ofℝnwith‖μ‖<∞, the analytic Feynman integral ofFexists, although the analytic Feynman integral,limz→−iqIaw(F;z)=limz→−iq(z/2π)n/2∫ℝnf(u→)exp{−(z/2)|u→|2}du→, do not always exist for bounded cylinder functionsF(x)=f((h1,x)∼,...,(hn,x)∼),x∈B. We prove a change of scale formula for Wiener integrals ofFon the abstract Wiener space.

scholarly journals A Rotation on Wiener Space with Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Jae Gil Choi ◽  
Seung Jun Chang
Keyword(s):  
Feynman Integral ◽  
Wiener Measure ◽  
Wiener Space ◽  
Fundamental Result ◽  
Convolution Product ◽  
Generalized Convolution ◽  
Analytic Feynman Integral ◽  
Generalized Analytic Feynman Integral ◽  
Wiener Spaces

We first investigate a rotation property of Wiener measure on the product of Wiener spaces. Next, using the concept of the generalized analytic Feynman integral, we define a generalized Fourier-Feynman transform and a generalized convolution product for functionals on Wiener space. We then proceed to establish a fundamental result involving the generalized transform and the generalized convolution product.

scholarly journals Parts formulas involving conditional Feynman integrals

2002 ◽  
Vol 65 (3) ◽  
pp. 353-369 ◽  
Author(s):  
Seung Jun Chang ◽  
David Skoug
Keyword(s):  
Basic Result ◽  
Feynman Integral ◽  
Wiener Space ◽  
Integration By Parts ◽  
Feynman Integrals ◽  
First Variation ◽  
Basic Formula ◽  
Analytic Feynman Integral ◽  
The First Variation

In this paper we first obtain a basic formula for the conditional analytic Feynman integral of the first variation of a functional on Wiener space. We then apply this basic result to obtain several integration by parts formulas for conditional analytic Feynman integrals and conditional Fourier-Feynman transforms.

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