论文标题
fock-bargmann表示的分解代数
Resolvent algebra in Fock-Bargmann representation
论文作者
论文摘要
D. Buchholz和H. Grundling引入了与Sympletic Space $（X，σ）$相关的分解代数$ \ Mathcal {R}（X，σ）$，作为量子力学中规范通勤关系（CCR）的方便模型。我们首先研究了$ \ Mathcal {r}（\ Mathbb {c}^n，σ）$的代表，并在Fock-Bargmann空间上的整个Toeplitz代数内的标准符号表格$σ$。我们证明$ \ Mathcal {r}（\ Mathbb {C}^n，σ）$本身是一个toeplitz代数。在R. Werner的对应理论的意义上，我们确定了其相应的移位不变和符号的封闭空间。最后，我们讨论了分解代数$ \ mathcal {r}（\ Mathcal {h}，\tildeσ）$的无限尺寸符号分离的Hilbert Space $（\ Mathcal {h}，\Tildeσ）$。更准确地说，我们在无限的许多变量中，在Fock-Bargmann空间上找到了$ \ Mathcal {r}（\ Mathcal {h}，\tildeσ）$的表示形式。
The resolvent algebra $\mathcal{R}(X, σ)$ associated to a symplectic space $(X, σ)$ was introduced by D. Buchholz and H. Grundling as a convenient model of the canonical commutation relation (CCR) in quantum mechanics. We first study a representation of $\mathcal{R}(\mathbb{C}^n, σ)$ with the standard symplectic form $σ$ inside the full Toeplitz algebra over the Fock-Bargmann space. We prove that $\mathcal{R}(\mathbb{C}^n, σ)$ itself is a Toeplitz algebra. In the sense of R. Werner's correspondence theory we determine its corresponding shift-invariant and closed space of symbols. Finally, we discuss a representation of the resolvent algebra $\mathcal{R}(\mathcal{H}, \tildeσ)$ for an infinite dimensional symplectic separable Hilbert space $(\mathcal{H}, \tildeσ)$. More precisely, we find a representation of $\mathcal{R}(\mathcal{H}, \tildeσ)$ inside the full Toeplitz algebra over the Fock-Bargmann space in infinitely many variables.
