  We report exact results for the partition function for free Dirac fermions on
a half line with physically sensible boundary conditions. An exact effective
action for general backscattering amplitudes is derived. The action also
includes the effects of both a (time-dependent) forward scattering amplitude
and a dynamical chiral twist of the fermion boundary conditions. For a small
backscattering amplitude, the effective action has the expected boundary
Sine-Gordon form. We discuss applications of our results to one-dimensional
Fermi systems with local backscattering.
