Mathematical construction of chiral anomaly

AbstractChiral anomaly is constructed with mathematical rigor by means of the lattice regularization. To this end, the quantized Dirac fermion on a torus coupled with an external gauge field with an arbitrary topology is analyzed. It is claimed that in order to complete the rigorous lattice approach to the chiral anomaly, the heat kernel regularization for the integrand should be introduced independently of the lattice regularization for the path measure