Relative zeta-determinants of Dirac Laplacians on a half-infinite cylinder with boundary conditions in the smooth, self-adjoint Grassmannian

In this paper we compute the relative zeta-determinants of Dirac Laplacians on a half-infinite cylinder when the Dirichlet boundary condition and the boundary condition belonging to the smooth, self-adjoint Grassmannian are imposed on the bottom of the half-infinite cylinder. We next apply this result to compute the relative zeta-determinants of Dirac Laplacians on a manifold with cylindrical end when the boundary condition belonging to the smooth, self-adjoint Grassmannian is imposed on the bottom of the half-infinite cylinder.