论文标题
callias运算符的分解的跟踪类属性
Trace Class Properties of Resolvents of Callias Operators
论文作者
论文摘要
我们提供一个家庭的条件$ \ left（a \ left（x \ right）\右）_ {x \ in \ mathbb {r}^{d}} $ seffAdexhaphapchaint Operators in $ h^{r} = \ mathbb {c}} $ d = ic \ nabla+a \ left（x \ right）$满足$ \ left（d^{\ ast} d+1 \ right）^{ - n} - n} - \ left（dd^{\ ast} +1 $ l^2 \ left（\ mathbb {r}^{d}，h^{r} \ right）$。在这里，$ c \ nabla $是与clifford乘法$ c $ C $ r $ r $相关的零零操作员$ l^2 \ left（\ mathbb {r}^{d}，h^{r} \ right）$。
We present conditions for a family $\left(A\left(x\right)\right)_{x\in\mathbb{R}^{d}}$ of self-adjoint operators in $H^{r}=\mathbb{C}^{r}\otimes H$ for a separable complex Hilbert space $H$, such that the Callias operator $D=ic\nabla+A\left(X\right)$ satisfies that $\left(D^{\ast}D+1\right)^{-N}-\left(DD^{\ast}+1\right)^{-N}$ is trace class in $L^2\left(\mathbb{R}^{d},H^{r}\right)$. Here, $c\nabla$ is the Dirac operator associated to a Clifford multiplication $c$ of rank $r$ on $\mathbb{R}^{d}$, and $A\left(X\right)$ is fibre-wise multiplication with $A\left(x\right)$ in $L^2\left(\mathbb{R}^{d},H^{r}\right)$.
