论文标题
$ c^*$ - 费米系统和详细余额
$C^*$-fermi systems and detailed balance
论文作者
论文摘要
产品和对角线状态的系统理论是针对$ \ mathbb z_2 $ - 加入$*$ - 代数的张量产品的，以及$ \ Mathbb Z_2 $ - 加入$ C^*$ - 代数。作为实现此目标的初步步骤，我们提供了$ \ Mathbb Z_2 $ - 加入的$ C^*$ - 代数的{\ it fermionic $ c^*$ - 张量产品}的构建。然后研究von Neumann代数之间的正线性图的扭曲二元，并应用于在无限的费米晶格上解决阳性问题。最后，这些结果用于在一般$ c^*$ - 具有$ \ mathbb Z_2 $等级的系统中，通过将这样的系统视为复合系统的一部分并使用对基因态，将其定义为fermionic的详细余额（其中包括通常的张量产品作为特定情况）的定义。
A systematic theory of product and diagonal states is developed for tensor products of $\mathbb Z_2$-graded $*$-algebras, as well as $\mathbb Z_2$-graded $C^*$-algebras. As a preliminary step to achieve this goal, we provide the construction of a {\it fermionic $C^*$-tensor product} of $\mathbb Z_2$-graded $C^*$-algebras. Twisted duals of positive linear maps between von Neumann algebras are then studied, and applied to solve a positivity problem on the infinite Fermi lattice. Lastly, these results are used to define fermionic detailed balance (which includes the definition for the usual tensor product as a particular case) in general $C^*$-systems with gradation of type $\mathbb Z_2$, by viewing such a system as part of a compound system and making use of a diagonal state.
