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Morozov, Sergey; Müller, David (2017): Lower bounds on the moduli of three-dimensional Coulomb-Dirac operators via fractional Laplacians with applications. In: Journal of Mathematical Physics, Vol. 58, No. 7, 72302
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For nu is an element of [0, 1], let D-nu be the distinguished self-adjoint realisation of the threedimensional Coulomb-Dirac 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 D-nu vertical bar >= C-nu root-Delta, where C-nu 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 K-lambda > 0 such that the estimate vertical bar D-1 vertical bar >= K(lambda)a(lambda-1) (-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 electron-positron field and obtain Cwickel-LiebRozenblum and Lieb-Thirring type estimates on the negative eigenvalues of perturbed projected massless Coulomb-Dirac operators in the Furry picture. We also study the existence of a virtual level at zero for such projected operators. Published by AIP Publishing.