2020
DOI: 10.1142/s0217732320400088
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The Casimir energy anomaly for a point interaction

Abstract: The Casimir energy for a massless, neutral scalar field in presence of a point interaction is analyzed using a general zeta-regularization approach developed in earlier works. In addition to a regular bulk contribution, there arises an anomalous boundary term which is infinite despite renormalization. The intrinsic nature of this anomaly is briefly discussed.

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Cited by 6 publications
(13 citation statements)
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“…Each extension is labeled by the single real-valued extension parameter α, which, eventually, will restrict the possible eigenfunctions (labeled by pairwise index u ωα ) of a Hamiltonian. Now we can go back and combine the self-adjoint H 0α with otherḢ l (l 1) and obtain the analogue of resolution (29) for the total extended Hamiltonian as a completely self-adjoint operator:…”
Section: Self-adjoint Extensionmentioning
confidence: 99%
See 1 more Smart Citation
“…Each extension is labeled by the single real-valued extension parameter α, which, eventually, will restrict the possible eigenfunctions (labeled by pairwise index u ωα ) of a Hamiltonian. Now we can go back and combine the self-adjoint H 0α with otherḢ l (l 1) and obtain the analogue of resolution (29) for the total extended Hamiltonian as a completely self-adjoint operator:…”
Section: Self-adjoint Extensionmentioning
confidence: 99%
“…Similar singular configurations were previously analyzed in the recent literature. Among the notable are the effective action of pointlike interactions [25], the delta-potentials at finite temperature [26], Casimir interactions of manifolds with diverse codimensionalities [27], the Casimir effect with a boundary hyperplane [28], zeta regularization approach to various Casimir problems [10][11][12]29], and so forth.…”
Section: Introductionmentioning
confidence: 99%
“…The main object of investigation is the vacuum polarization, namely the renormalized expectation value of the field squared at any spacetime point. This is computed implementing the ζ-regularization technique in the formulation outlined in [42] (see also [43][44][45]), which allows to derive explicit integral representations in all cases of interest. These representations are then employed to determine the asymptotic behavior of the vacuum polarization close to the hyperplane and far away from it.…”
Section: Introductionmentioning
confidence: 99%
“…The Casimir physics of scalar fields in presence of point-like impurities was investigated in a number of previous works, mentioned in Section 9 of [1]. In particular, the case of a quantized scalar field with a single point-like impurity was discussed in our papers [2,3], making reference to the zeta regularization approach to Casimir physics (see again the books [7,8] and the references cited therein, accounting for the long story of this approach). In [2] we determined the VEV of all components of the stress-energy tensor and, in particular, of the energy density (for arbitrary values of the conformal parameter ξ).…”
Section: Introductionmentioning
confidence: 99%
“…In [2] we determined the VEV of all components of the stress-energy tensor and, in particular, of the energy density (for arbitrary values of the conformal parameter ξ). In [3], one of us (D.F.) examined the VEV of the total energy for the same system.…”
Section: Introductionmentioning
confidence: 99%