https://doi.org/10.1140/epjp/s13360-025-06096-4
Regular Article
Vacuum polarization effects of pointlike impurity
Department of Theoretical Physics, M.V.Lomonosov Moscow State University, 119991, Moscow, Russian Federation
Received:
26
December
2024
Accepted:
4
February
2025
Published online:
21
February
2025
We develop precise formulation for the effects of vacuum polarization near a pointlike source with a zero-range (
-like) potential in three spatial dimensions. There are different ways of introducing -interaction in the framework of quantum theory. We discuss the approach based on the concept of self-adjoint extensions of densely defined symmetric operators. Within this approach, we consider the real massive scalar field in three-dimensional Euclidean space with a single extracted point. Appropriate boundary conditions, imposed at this point, enable one to consider all self-adjoint extensions of 
as operators which can describe a pointlike source with a zero-range potential. In this framework, we compute the renormalized vacuum expectation value of the field square 
and the renormalized vacuum average of the scalar-field’s energy-momentum tensor 
. Asymptotic cases are discussed in detail.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
