  We present a new regularization method, for d dim (Euclidean) quantum field
theories in the continuum formalism, based on the domain wall configuration in
(1+d) dim space-time. It is inspired by the recent progress in the chiral
fermions on lattice. The wall "height" is given by 1/M, where M is a
regularization mass parameter and appears as a (1+d) dim Dirac fermion mass.
The present approach gives a {\it thermodynamic view} to the domain wall or the
overlap formalism in the lattice field theory. We will show qualitative
correspondence between the present continuum results and those of lattice. The
extra dimension is regarded as the (inverse) {\it temperature} t. The domains
are defined by the {\it 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
chiral gauge theory as examples. Especially the consistent and covariant
anomalies are correctly obtained.
