  We derive the bosonization rules for free fermions on a half-line with
physically sensible boundary conditions for Luttinger fermions. We use
path-integral methods to calculate the bosonized fermionic currents on the
half-line and derive their commutation relations for a system with a boundary.
We compute the fermion determinant of the fermionic fluctuations for a system
with a boundary using Forman's approach. We find that the degrees of freedom
induced at the boundary do not to modify the commutation relations of the bulk.
We give an explicit derivation of the bosonization rules for the fermion
operators for a system with boundaries. We derive a set of bosonization rules
for the Fermi operators which include the explicit effect of the boundaries and
of boundary degrees of freedom. As a byproduct, we calculate the one-particle
Green's function and determine the effects of the boundaries on its analytic
structure.
