I will talk about a simple physical derivation of the so-called Atiyah-Patodi-Singer (APS) index theorem. The derivation is just a minor modification of Fujikawa’s argument for the axial U(1) anomaly once we we understand a physical interpretation of the APS boundary condition. It is based on my recent work with Shun K. Kobayashi https://arxiv.org/abs/2103.10654