Some Recent Results on Contact or Point Supported Potentials

Nieto, L. M.; Gadella, M.; Guilarte, J. Mateos; Munõz-Castañeda, J. M.; Romaniega, C.

doi:10.1007/978-3-030-53305-2_14

Cited by 2 publications

(2 citation statements)

References 14 publications

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“…At the same time, such singular potentials can often be interpreted as limits (in resolvent sense) of sharply peaked, regular potentials. More technical details on these subjects can be found, e.g., in [13][14][15][16][17]. Nowadays, a quite rich literature is available regarding the analysis of Casimir-type settings with external zero-range potentials.…”

Section: Introductionmentioning

confidence: 99%

Vacuum Polarization with Zero-Range Potentials on a Hyperplane

Fermi

2021

Universe

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The quantum vacuum fluctuations of a neutral scalar field induced by background zero-range potentials concentrated on a flat hyperplane of co-dimension 1 in (d+1)−dimensional Minkowski spacetime are investigated. Perfectly reflecting and semitransparent surfaces are both taken into account, making reference to the most general local, homogeneous and isotropic boundary conditions compatible with the unitarity of the quantum field theory. The renormalized vacuum polarization is computed for both zero and non-zero mass of the field, implementing a local version of the zeta regularization technique. The asymptotic behaviors of the vacuum polarization for small and large distances from the hyperplane are determined to leading order. It is shown that boundary divergences are softened in the specific case of a pure Dirac delta potential.

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Section: Introductionmentioning

confidence: 99%

Vacuum Polarization with Zero-Range Potentials on a Hyperplane

Fermi

2021

Universe

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show abstract

“…At the same time, such singular potentials can often be interpreted as limits (in resolvent sense) of sharply peaked, regular potentials. More technical details on these subjects can be found, e.g., in [4,5,48,50]. Nowadays, a quite rich literature is available regarding the analysis of Casimir-type settings with external zero-range potentials.…”

Section: Introductionmentioning

confidence: 99%

Vacuum polarization with zero-range potentials on a hyperplane

Fermi

2021

Preprint

View full text Add to dashboard Cite

The quantum vacuum fluctuations of a neutral scalar field induced by background zero-range potentials concentrated on a flat hyperplane of co-dimension 1 in (d + 1)-dimensional Minkowski spacetime are investigated. Perfectly reflecting and semitransparent surfaces are both taken into account, making reference to the most general local, homogeneous and isotropic boundary conditions compatible with the unitarity of the quantum field theory. The renormalized vacuum polarization is computed for both zero and non-zero mass of the field, implementing a local version of the zeta regularization technique. The asymptotic behaviours of the vacuum polarization for small and large distances from the hyperplane are determined to leading order. It is shown that boundary divergences are soften in the specific case of a pure Dirac delta potential.

show abstract

Some Recent Results on Contact or Point Supported Potentials

Cited by 2 publications

References 14 publications

Vacuum Polarization with Zero-Range Potentials on a Hyperplane

Vacuum Polarization with Zero-Range Potentials on a Hyperplane

Vacuum polarization with zero-range potentials on a hyperplane

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