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Symmetry 2018, 10(2), 38; https://doi.org/10.3390/sym10020038

Local Casimir Effect for a Scalar Field in Presence of a Point Impurity

1,2,†
and
1,2,*
1
Dipartimento di Matematica, Università di Milano, Via C. Saldini 50, I-20133 Milano, Italy
2
Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Via G. Celoria 16, I-20133 Milano, Italy
davide.fermi@unimi.it.
*
Author to whom correspondence should be addressed.
Received: 28 December 2017 / Revised: 19 January 2018 / Accepted: 22 January 2018 / Published: 26 January 2018
(This article belongs to the Special Issue Casimir Physics and Applications)
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Abstract

The Casimir effect for a scalar field in presence of delta-type potentials has been investigated for a long time in the case of surface delta functions, modelling semi-transparent boundaries. More recently Albeverio, Cacciapuoti, Cognola, Spreafico and Zerbini have considered some configurations involving delta-type potentials concentrated at points of R 3 ; in particular, the case with an isolated point singularity at the origin can be formulated as a field theory on R 3 \ { 0 } , with self-adjoint boundary conditions at the origin for the Laplacian. However, the above authors have discussed only global aspects of the Casimir effect, focusing their attention on the vacuum expectation value (VEV) of the total energy. In the present paper we analyze the local Casimir effect with a point delta-type potential, computing the renormalized VEV of the stress-energy tensor at any point of R 3 \ { 0 } ; for this purpose we follow the zeta regularization approach, in the formulation already employed for different configurations in previous works of ours. View Full-Text
Keywords: Local Casimir effect; renormalization; zeta regularization; delta-interactions Local Casimir effect; renormalization; zeta regularization; delta-interactions
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Fermi, D.; Pizzocchero, L. Local Casimir Effect for a Scalar Field in Presence of a Point Impurity. Symmetry 2018, 10, 38.

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