On the stability and spectral properties of the two-dimensional Brown–Ravenhall operator with a short-range potential

The Brown–Ravenhall operator was initially proposed as an alternative to describe the fermion–fermion interaction via Coulomb potential and subject relativity. This is defined in terms of associated Dirac projection onto positive spectral subspace free operator. In this paper, we propose analyze a modified version two-dimensions. More specifically, consider with short-range attractive given by Bessel–Macdonald function (also known K0-potential) using Foldy–Wouthuysen unitary transformation. Initially, prove that two-dimensional K0-potential bounded from below when coupling constant specified critical value (a property also referred stability). A major feature model fact it does not cease be even if above value. We investigate nature spectrum operator, particular location essential spectrum, existence eigenvalues, which are either isolated or embedded it.