Projeto Futuras Cientistas E Os Desafios No Ensino De Engenharia

Santos, Mathews Lima dos; Picchi, Ivan Bezerra de Mello; Araújo, Helen Rodrigues; Siqueira, Lucas Oliveira; Santos, Tiago Felipe de Abreu

doi:10.29327/aconemi.412339

Cited by 1 publication

(1 citation statement)

References 2 publications

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“…In recent literature, various singular configurations have been studied, including point-like interactions [28], delta potentials at finite temperature [29], Casimir interactions of manifolds with different codimensions [30], Casimir effect with a boundary hyperplane [32,33], and Casimir problems approached using Zeta-regularization [11,12].…”

Section: Introductionmentioning

confidence: 99%

Zero-Range Potentials: Delta-Like Barrier Versus Self-Adjoint Extension

Grats

Spirin

2022

Moscow Univ. Phys.

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We develop precise formulation for the effects of vacuum polarization near a pointlike source with a zero-range (δ-like) potential in three spatial dimensions. There are different ways of introducing δ-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 φ 2 (x) ren and the renormalized vacuum average of the scalar-field's energy-momentum tensor Tµν (x) ren. Asymptotic cases are discussed in detail.

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