BOSONIZATION RULES IN 1 2+1-DIMENSIONS

We derive the bosonization rules for free fermions on a half-line with physically sensible boundary conditions for Luttinger fermions, We us e path-integral methods to calculate the bosonized fermionic currents on the half-line and derive their commutation relations for a system w ith a boundary. We compute the fermion determinant of the fermionic fl uctuations for a system with a boundary using Forman's approach. We fi nd that the degrees of freedom induced at the boundary do not to modif y the commutation relations of the bulk. We give an explicit derivatio n of the bosonization rules for the fermion operators for a system wit h boundaries. We derive a set of bosonization rules for the Fermi oper ators which include the explicit effect of the boundaries and of bound ary degrees of freedom. As a byproduct, we calculate the one-particle Green function and determine the effects of the boundaries on its anal ytic structure.