AI 中文总结
本文将Freed与Hopkins的SPT相分类ansatz推广为适合同构晶体学对称性的完全等变版本，证明存在对应等变FTI映射，论证该等变方案比原空间对称扩展更具自然性。
AI 中文摘要
Freed与Hopkins提出了一种ansatz（近似方法），用于利用可逆场论结合从自由费米子相出发的自然自由到相互作用（Free to Interacting, FTI）映射来分类相互作用SPT相。该ansatz已被推广以包含晶体相和晶体等价原理（Crystalline Equivalence Principle, CEP）。然而，受弱自由费米子和FTI的CEP失效的启发，本文将Freed与Hopkins的原始ansatz推广为适合同构晶体学对称性的完全等变版本，并证明存在从同构晶体弱自由费米子出发的自然等变FTI映射。我们进一步讨论了该等变ansatz为何在数学和物理上比Freed与Hopkins提出的空间对称性扩展更自然，以及完全等变性为何应优于CEP成立。
英文摘要
Freed and Hopkins developed an ansatz for classifying interacting SPT phases using invertible field theories with a natural Free to Interacting (FTI) map from free fermion phases. This ansatz has been generalized to include crystalline phases and a crystalline equivalence principle (CEP). However, motivated by failure of the CEP for weak free fermions and the FTI, here we generalize the original Freed and Hopkins ansatz to a fully equivariant version for symmorphic crystallographic symmetries and show there is a natural equivariant FTI map from symmorphic crystalline weak free fermions. We further discuss why this equivariant ansatz is both mathematically and physically more natural than the spatial symmetry extension by Freed and Hopkins and why full equivariance should hold over the CEP.
Comments10 pages; comments very much welcome!
