Positivity of the two-dimensional Brown-Ravenhall operator

Abstract

We determine the critical coupling of the two-dimensional Brown-Ravenhall operator with Coulomb potential. Boundedness from below has essentially been proven by Bouzouina, whose work however contains a trivial error leading to a wrong constant exactly one half of the actual critical constant. Furthermore we show that the operator is in fact positive. Our proof of that is for the most part analogous to Tix's proof of the corresponding result for the three-dimensional operator.