On the Absence of Bound States for a Planar Massless Brown–Ravenhall-Type Operator

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 in Ref. [1]. Based on Relativistic Hardy Inequality, we prove that this operator has no bound states if γ γ crit (subcritical region), where γ is a coupling constant.