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In this paper we discuss the refined analytic torsion on an odd dimensionalcompact oriented Riemannian manifold with boundary under some assumption. Forthis purpose we introduce two boundary conditions which are complementary toeach other and well-posed for the odd signature operator $\mathcal{B}$ in thesense of Seeley. We then show that the zeta-determinants of $\mathcal{B}^2$ andeta-invariants of $\mathcal{B}$ subject to these boundary conditions are welldefined by using the method of the asymptotic expansions of the traces of theheat kernels. We use these facts to define the refined analytic torsion on acompact manifold with boundary and show that it is invariant on the change ofmetrics in the interior of the manifold. We finally describe the refinedanalytic torsion under these boundary conditions as an element of thedeterminant line.

The refined analytic torsion and a well-posed boundary condition for the odd signature operator