  Inspired by the work of Boris Vertman on refined analytic torsion for
manifolds with boundary, in this paper we extend the construction of the
Cappell-Miller analytic torsion to manifolds with boundary. We also compare it
with the refined analytic torsion on manifolds with boundary. As a byproduct of
the gluing formula for refined analytic torsion and the comparison theorem for
the Cappell-Miller analytic torsion and the refined analytic torsion, we
establish the gluing formula for the Cappell-Miller analytic torsion in the
case that the Hermitian metric is flat.
