Abstract
The formulation of the Casimir effect without cutoffs is discussed. Our derivation emphasizes the decisive role of the free-space electromagnetic energy density. The zero point energy arises as an energy per unit volume, i.e., as local (in x space) energy density. It is given by the vaccum expectation value of the free-space Hamiltonian density in the Fock representation corresponding to the non-trivial geometry. The two Fock representations corresponding to the system with and without plates are proved to be inequivalent.
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Scharf, G., Wreszinski, W.F. On the Casimir effect without cutoff. Found Phys Lett 5, 479–487 (1992). https://doi.org/10.1007/BF00690428
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DOI: https://doi.org/10.1007/BF00690428