Reflection positivity and invertible topological phases
Reflection positivity and invertible topological phases
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DOI：
10.2140/gt.2021.25.1165
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发表时间：
2016-04
影响因子：
2
通讯作者：
D. Freed;M. Hopkins
中科院分区：
文献类型：
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作者：
D. Freed;M. Hopkins
我们实现了可逆拓扑量子场理论的反射正性（wick - rotational uniform）的扩展版本，并利用稳定同伦理论计算了变形类的阿贝尔群。我们将这些场论考虑应用于晶格系统，假设低能量有效场论近似的存在性和有效性，从而得出了对称保护拓扑（SPT）相群在Thom’s bordism谱中的一般公式；唯一的输入是维度和对称群。我们提供了物理相关维度的费米子系统的计算。其他主题包括量子场论中的对称性，相对论性的10重方式，相对论性自由费米子的同伦理论，以及拓扑自旋统计定理。
We implement an extended version of reflection positivity (Wick-rotated unitarity) for invertible topological quantum field theories and compute the abelian group of deformation classes using stable homotopy theory. We apply these field theory considerations to lattice systems, assuming the existence and validity of low energy effective field theory approximations, and thereby produce a general formula for the group of Symmetry Protected Topological (SPT) phases in terms of Thom's bordism spectra; the only input is the dimension and symmetry group. We provide computations for fermionic systems in physically relevant dimensions. Other topics include symmetry in quantum field theories, a relativistic 10-fold way, the homotopy theory of relativistic free fermions, and a topological spin-statistics theorem.