Let M1 and M2 be two Riemannian manifolds each of which has the boundary N. Consider the Laplacian on M1 and M2 augmented with Dirichlet boundary conditions on N. A natural question to ask is whether there is any relation between spectral properties of the Laplacian on M1, M2, and the Laplacian on the manifold M (without boundary) obtained by gluing together M1 and M2, namely M = M1 ∪N M2. A partial answer is given by the Burghelea-Friedlander-Kappeler-gluing formula for zeta-determinants. This formula contains an (in general) unknown polynomial which is completely determined by some data on a collar neighborhood of the hypersurface N. In this talk, I present results for the polynomial in terms of suitable geometric tensors on N. Choosing M1, M2 and M as appropriate, results in a gluing formula for Casimir energies.
Conflicts of Interest
The authors declare no conflict of interest.
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