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arXiv · 2209.04559

On the absence of bound states for a planar massless Brown-Ravenhall-type operator

M. B. Alves·O. M. Del Cima·D. H. T. Franco
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Abstract

We address the question of the existence of bound states for a suitably projected two-dimensional massless Dirac operator in the presence of a Bessel-Macdonald potential (also known as $K_0$-potential potential), raised by De Lima, Del Cima and Miranda, in Eur.Phys.J. B (2020) 93, 187. Based on Relativistic Hardy Inequality, we prove that this operator has no bound states if $\gamma \leqslant \gamma_{\rm crit}$ (subcritical region), where $\gamma$ is a coupling constant.

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M. B. Alves, O. M. Del Cima, D. H. T. Franco. 2022-09-09. On the absence of bound states for a planar massless Brown-Ravenhall-type operator. https://doi.org/10.1007/s00601-022-01763-z

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