  The refined analytic torsion on compact Riemannian manifolds with boundary
has been discussed by B. Vertman and the authors, but these two constructions
are completely different. Vertman used a double of de Rham complex consisting
of the minimal and maximal closed extensions of a flat connection and the
authors used well-posed boundary conditions ${\mathcal P}_{-, {\mathcal
L}_{0}}$, ${\mathcal P}_{+, {\mathcal L}_{1}}$ for the odd signature operator.
In this paper we compare these two constructions by using the BFK-gluing
formula for zeta-determinants, the adiabatic method for stretching cylinder
part near boundary and the deformation method used in [6], when the odd
signature operator comes from a Hermitian flat connection and all de Rham
cohomologies vanish.
