New regularization using domain wall

We present a new regularization method, for d-dimensional (Euclidean) quant um field theories in the continuum formalism, based on the domain wall conf iguration in (1 + d)-dimensional space-time, it is inspired by the recent p rogress in chiral fermions on a lattice. The wall "thickness" is given by 1 /M, where hi is a regularization mass parameter and appears as a (1 + d)-di mensional Dirac fermion mass. The present approach gives a thermodynamic vi ew on the domain wall or overlap formalism in 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) temp erature a. The domains are defined by the directions of the "system evoluti on", not by the sign of dl as in the original overlap formalism. Physically the parameter M controls both the chirality selection and the dimensional reduction to d dimensions (domain wall formation). From the point of regula rization, the limit Mt --> 0 regularizes the infra-red behavior whereas the condition on the momentum (k(mu)) integral, \k(mu)\ less than or equal to M, regularizes the ultra-violet behavior, To check that the new regularizat ion works correctly, we take four-dimensional QED and two-dimensional chira l gauge theory as examples. Especially the consistent and covariant anomali es are correctly obtained. The choice of solutions of the higher dimensiona l Dirac equation characterizes the two anomalies. The projective properties of the positive and negative energy free solutions are exploited in calcul ation. Some integral functions, the incomplete gamma functions and the gene ralized hypergeometric functions characteristically appear in this new regu larization procedure. (C) 2000 Elsevier Science B.V. All rights reserved.