论文标题
a $ \ mathbb {z} _ {2} $ - 拓扑索引为$ \ mathbb {z} _ {2} $ - 状态索引
A $\mathbb{Z}_{2}$-Topological Index as a $\mathbb{Z}_{2}$-State Index
论文作者
论文摘要
在无限尺寸的自dual $ \ mathrm {car} $ $ c^{*} $ - 代数中描述$ \ Mathbb {z}^{d} $ lattice的费米子 - 我们与众所周知的araki-evans $σ（p_ {1}，p_ {2}）中的fermions描述费米子。 $ \ mathbb {z} _ {2} $ - 准无效率状态的索引，并以状态而不是基础预测来重写它。此外，我们重新制定了将FOCK表示与指数平价等效的结果重新调整，将GNS表示等同的等价与相关的指数均衡相关联。
Within the setting of infinite dimensional self-dual $\mathrm{CAR}$ $C^{*}$-algebras describing fermions in the $\mathbb{Z}^{d}$-lattice, we depart from the well-known Araki-Evans $σ(P_{1},P_{2})$ $\mathbb{Z}_{2}$-index for quasi-free fermion states and rewrite it in terms of states, rather than in terms of basis projections. Furthermore, we reformulate results which relate equivalences of Fock representations with the index parity into results which relate equivalences of GNS representations and the associated index parity.
