Morozov, Sergey; Müller, David
(2017):
Lower bounds on the moduli of threedimensional CoulombDirac operators via fractional Laplacians with applications.
In: Journal of Mathematical Physics, Vol. 58, No. 7, 72302

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Abstract
For nu is an element of [0, 1], let Dnu be the distinguished selfadjoint realisation of the threedimensional CoulombDirac operator i alpha center dot del nu vertical bar center dot vertical bar(1). For nu is an element of [0, 1), we prove the lower bound of the form vertical bar Dnu vertical bar >= Cnu rootDelta, where Cnu is found explicitly and is better than in all previous studies on the topic. In the critical case nu = 1, we prove that for every lambda is an element of[0, 1), there exists Klambda > 0 such that the estimate vertical bar D1 vertical bar >= K(lambda)a(lambda1) (Delta)(lambda/2)  a(1) holds for all a > 0. As applications, we extend the range of coupling constants in the proof of the stability of the relativistic electronpositron field and obtain CwickelLiebRozenblum and LiebThirring type estimates on the negative eigenvalues of perturbed projected massless CoulombDirac operators in the Furry picture. We also study the existence of a virtual level at zero for such projected operators. Published by AIP Publishing.