컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0224 |
|---|---|
| 분류(Section) | Contributed Talk |
| 분과(Session) | (AN) Analysis (AN) |
| 발표시간(Time) | 19th-A-10:00 -- 10:20 |
| 영문제목 (Title(Eng.)) |
A generalized analytic conditional Feynman integral with its applications |
| 저자(Author(s)) |
Dong Hyun Cho1 Kyonggi University1 |
| 초록본문(Abstract) | Let $C^{\mathbb B}[a,b]$ denote an analogue of Wiener space over paths in abstract Wiener space $\mathbb B$, the space of $\mathbb B$-valued continuous functions on $[a,b]$. Let $W(x)=\{x(t_n)\}_{n=0}^\infty\in \mathbb B^{\aleph_0}$ for $x\in C^{\mathbb B}[a,b]$, where $\{t_n\}_{n=0}^\infty$ is a strictly increasing sequence in $[a,b]$ with $t_0=a$ and $\lim_{n\to\infty}t_n=b$. In this talk, we introduce a positive finite measure with scale on $C^{\mathbb B}[a,b]$ which is a generalized analogue of Wiener measure. Then we extend the time integral (Riemann integral) to a Riemann-Stieltjes integral which is more generalized time integral on $C^{\mathbb B}[a,b]$. Finally, using a simple formula for calculating a Radon-Nikodym derivative similar to the conditional Wiener integral of functions on $C^{\mathbb B}[a,b]$ given $W$ which has an initial weight, we evaluate a generalized $L_p$-analytic conditional Feynman integral of the extended time integral. The established $L_p$-analytic conditional Feynman integrals are interested in quantum mechanics, especially in the Feynman integration theory. |
| 분류기호 (MSC number(s)) |
28C20 |
| 키워드(Keyword(s)) | Abstract Wiener space, analogue of Wiener space, analytic conditional Feynman integral, analytic Feynman integral, Wiener space, Wiener space over paths in abstract Wiener space |
| 강연 형태 (Language of Session (Talk)) |
Korean |