컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0529 |
|---|---|
| 분류(Section) | Contributed Talk |
| 분과(Session) | Functional Analysis and Applications (SS-09) |
| 영문제목 (Title(Eng.)) |
[CANCELLED] Fedosov quantization and time operators |
| 저자(Author(s)) |
Job A. Nable1, Eric A. Galapon2 Mathematics Department, Ateneo De Manila University1, National Institute of Physics, University of the Philippines, Diliman2 |
| 초록본문(Abstract) | We study the relation between time operators as it appears in the works of the second author and the theory of deformation quantization. In particular, it is pointed out that the functions appearing in time operators as kernels of integral operators are objects in the space $C^{\infty}(\mathbb R^2)[[\hbar]]$ of power series in $\hbar$ and that under the Weyl-Moyal star-product, we get the correspondence principle $[T_{\hbar}, H]_*=i\hbar\{{t}_0, H\},$ for a discrete or semibounded Hamiltonian $H$. Secondly, we present results where an attempt to put the time kernel functions into the deformation quantization setting via the construction of Fedosov is carried out. Two abelian connections $D_1$ and $D_2$ are identified on Weyl algebras bundle $\cal W$ consisting of series of the form $a=\sum_{k, i, j}(q, q')\hbar^ka_{k, i, j}(y^1)^{\alpha_1}(y^2)^{\alpha_2},$ where $(q, q')$ are coordinates of $M=\mathbb R^2$ and $y^1=\displaystyle\frac{\partial}{\partial q}, y^2=\displaystyle\frac{\partial}{\partial q'}$ are coordinates on the tangent space $T_{(q_0, q'_0)}(M).$ The Lie algebra ${\cal W}_D=\{a:Da=0\}$ will be shown to be Lie algebra isomorphic to ${\cal Z}=C^{\infty}(M)[|\epsilon|].$ The Weyl-Moyal star-product on ${\cal W}_D$ transfers to ${\cal Z} $ via this isomorphism. This provides a star-product on ${\cal Z} $ where the time kernel functions satisfy the canonical commutation relations in the sense of star-products. |
| 분류기호 (MSC number(s)) |
81S05, 81S10 |
| 키워드(Keyword(s)) | time operators, Fedosov deformation quantization, Weyl algebras |
| 강연 형태 (Language of Session (Talk)) |
English |