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- W4313480419 abstract "The local and global aspects of the Casimir effect for a scalar field in the presence of a point-like impurity were treated in our papers (Fermi and Pizzocchero in Symmetry 10(2):38, 2018; Fermi in Mod. Phys. Lett. A 35(03):2040008, 2020), using the zeta regularization method. A paper by Ziemian, recently published in (Ann. Henri Poincaré 22:1751–1781, 2021), discusses the Casimir effect for a scalar field in presence of one or two, extended or point-like impurities, using the Herdegen–Stopa approach. Ziemian claims that his result for the energy density with a single point-like impurity differs from that derived in Fermi and Pizzocchero (2018), ascribing the mismatch to a basic conceptual discrepancy. In the present work, we show that the formula in Ziemian (2021) for the energy density in the presence of a point-like impurity coincides (upon amending minor computational errors) with the formula of Fermi and Pizzocchero (2018) for the same quantity. In order to make our discussion self-contained, in the present paper we also survey some basic facts related to Fermi and Pizzocchero (2018), Fermi (2020), Ziemian (2021). This survey includes Schrödinger’s operators with point-like interactions, as described in the celebrated book (Solvable models in quantum mechanics, Springer, New York, 1988) by Albeverio et al., the zeta regularization method for a canonically quantized scalar field and the implementation of point-like interactions in this setting." @default.
- W4313480419 created "2023-01-06" @default.
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- W4313480419 date "2023-01-02" @default.
- W4313480419 modified "2023-10-05" @default.
- W4313480419 title "On the Casimir Effect with $$delta $$-Like Potentials, and a Recent Paper by K. Ziemian (Ann. Henri Poincaré, 2021)" @default.
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- W4313480419 doi "https://doi.org/10.1007/s00023-022-01263-0" @default.
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