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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