Heat-kernel approach to the overlap formalism

We present a new regularization method, for d dim (Euclidean) quantum field theories in the continuum formalism, based on the domain wall configuratio n in (1+d) dim space-time. It is inspired by the recent progress in the chi ral fermions on lattice. The wall "height" is given by 1/M, where M is a re gularization mass parameter and appears as a (1+d) dim Dirac fermion mass. The present approach gives a thermodynamic view to the domain wall or the o verlap formalism in the lattice field theory. We will show qualitative corr espondence between the present continuum results and those of lattice. The extra dimension is regarded as the (inverse) temperature t. The domains are defined by the directions of the "system evolvement", not by the sign of M as in the original overlap formalism. We take the 4 dim QED and 2 dim chir al gauge theory as examples. Especially the consistent and covariant anomal ies are correctly obtained.