Boundary triples for the Dirac operator with Coulomb-type spherically symmetric perturbations

Abstract

We determine explicitly a boundary triple for the Dirac operator H :Consequently we determine all the self-adjoint realizations of H in terms of the behaviour of the functions of their domain in the origin. When sup x |x||V(x)| ≤ 1, we discuss the problem of selecting the distinguished extension requiring that its domain is included in the domain of the appropriate quadratic form.

A Hardy-type inequality and some spectral characterizations for the Dirac–Coulomb operator

“…a complete description of all the self-adjoint extensions is given in [6,5]. Under some conditions on the size of the constants ν, µ, λ, a distinguished extension is selected by means of a Hardy-type inequality and a quadratic form approach.…”

“…Under some conditions on the size of the constants ν, µ, λ, a distinguished extension is selected by means of a Hardy-type inequality and a quadratic form approach. Nevertheless, in the particular case of the anomalous magnetic potential V(x) = ±iα • xβ|x| −1 such criteria do not appear to be strong enough to select any extension, see [6, Remark 1.10] and [5,Remark 1.6].…”

Self-adjointness for the MIT bag model on an unbounded cone

“…2.5] and [CP18, Thms. 1.1 and 1.2], [CP19]. We provide it in full detail for convenience of the reader and also because we need to cover some additional aspects.…”

Sharp exponential localization for solutions of the Perturbed Dirac Equation

“…10) are true; thanks to (4.7),(4.11) holds for a large enough k.Condition (1.16) holds obviously for r ∈ [ρ k0 , ρ k1 ] ∪ [ρ k3 , ρ k4 ]. For the case r ∈ [ρ k1 , ρ k2 ] we need to distinguish various cases: let s := 4(r − ρ k1 )/(ρ k+1 − ρ k ) and let us consider first the case s ∈ (0, (log ρ k ) −3/2 ).…”

“…In the massless case m = 0, ψ 0 is not in L 2 (R 3 ). We refer to [9,10] for a description of the functions in the domain of D 3 + V: we hope to investigate the phenomena described in this paper in the case that ǫ ≥ 1 in the future.…”