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 R3 ; in particular, the case with an isolated point singularity at the origin can be formulated as a field theory on R3\{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 R3\{0} ; for this purpose we follow the zeta regularization approach, in the formulation already employed for different configurations in previous works of ours.
Fermi, D., Pizzocchero, L. (2018). Local Casimir effect for a scalar field in presence of a point impurity. SYMMETRY, 10(2), 38 [10.3390/sym10020038].
Local Casimir effect for a scalar field in presence of a point impurity
Fermi D.
;
2018-01-01
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 R3 ; in particular, the case with an isolated point singularity at the origin can be formulated as a field theory on R3\{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 R3\{0} ; for this purpose we follow the zeta regularization approach, in the formulation already employed for different configurations in previous works of ours.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
