Atiyah-Patodi-Singer index theorem from axial anomaly

We give a very simple derivation of the Atiyah-Patodi-Singer (APS) index theorem and its small generalization by using path integral massless Dirac fermions. It is based on Fujikawa's argument for relation between axial anomaly Atiyah-Singer theorem, only minor modification that sufficient to show APS theorem. The key ingredient identification boundary condition as physical state vectors in Hilbert space fermion theory. $\eta$-invariant appears charge states.