The Atiyah-Patodi-Singer index theorem from the axial anomaly
The Atiyah-Patodi-Singer index theorem from the axial anomaly
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轴异常的 Atiyah-Patodi-Singer 指数定理
DOI：
10.1093/ptep/ptab061
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发表时间：
2021
影响因子：
3.5
通讯作者：
Kazuya Yonekura
中科院分区：
文献类型：
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作者：
Shun K. Kobayashi;Kazuya Yonekura
利用无质量狄拉克费米子的路径积分，给出了Atiyah-Patodi-Singer （APS）指标定理的一个非常简单的推导及其小推广。它是基于Fujikawa关于轴向异常与Atiyah-Singer指数定理之间关系的论证，对该论证稍加修改就足以证明APS指数定理。关键是确定APS边界条件，并将其推广为无质量费米子理论希尔伯特空间中的物理状态向量。aps不变量表现为物理态的轴向电荷。
We give a very simple derivation of the Atiyah–Patodi–Singer (APS) index theorem and its small generalization by using the path integral of massless Dirac fermions. It is based on Fujikawa’s argument for the relation between the axial anomaly and the Atiyah–Singer index theorem, and only a minor modification of that argument is sufficient to show the APS index theorem. The key ingredient is the identification of the APS boundary condition and its generalization as physical state vectors in the Hilbert space of the massless fermion theory. The APS-invariant appears as the axial charge of the physical states.