  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 the 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 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 the lattice. The extra
dimension is regarded as the (inverse) temperature t. The domains are defined
by the directions of the "system movement", not by the sign of M as in the
original overlap formalism. Physically the parameter M controls both the
chirality selection and the dimensional reduction to d dimension. From the
point of regularization, the limit $Mt\ra 0$ regularize the infra-red behaviour
whereas the condition on the momentum ($k^\m$) integral, $|k^\m|\leq M$,
regularize the ultra-violet behaviour.
  To check the new regularization works correctly, we take the 4 dim QED and 2
dim chiral gauge theory as examples. Especially the consistent and covariant
anomalies are correctly obtained. The choice of solutions of the higher dim
Dirac equation characterize the two anomalies. The projective properties of the
positive and negative energy free solutions are exploited in calculation. Some
integral functions, the incomplete gamma functions and the generalized
hypergeometric functions characteristically appear in the regularization
procedure.
