Vacuum polarization in d+1/2 dimensions

We study the main properties of the one-loop vacuum polarization function (Pi(alpha beta)) for spinor QED in 'd + 1/2 dimensions', i.e., with fields defined on M subset of Rd+1 such that M = {(x(0),..., x(d)) vertical bar x(d) >= 0}, with bag-like boundary conditions on the boundary partial derivative M = {(x(0),..., x(d)) vertical bar x(d) = 0}. We obtain an exact expression for the induced current due to an external constant electric field normal to the boundary. We show that, for the particular case of 2 + 1 dimensions, there is a transverse component for the induced current, which is localized on a region close to partial derivative M. This current is a parity breaking effect purely due to the boundary. (c) 2005 Elsevier B.V. All rights reserved.