Singular perturbations with boundary conditions and the Casimir effect in the half space
@article{Albeverio2010SingularPW, title={Singular perturbations with boundary conditions and the Casimir effect in the half space}, author={Sergio Albeverio and Guido Cognola and Mauro Spreafico and Sergio Zerbini}, journal={Journal of Mathematical Physics}, year={2010}, volume={51}, pages={063502} }
We study the self-adjoint extensions of a class of nonmaximal multiplication operators with boundary conditions. We show that these extensions correspond to singular rank 1 perturbations (in the sense of Albeverio and Kurasov [Singular Perturbations of Differential Operaters (Cambridge University Press, Cambridge, 2000)]) of the Laplace operator, namely, the formal Laplacian with a singular delta potential, on the half space. This construction is the appropriate setting to describe the Casimir…
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