We discuss the spectral properties of three-dimensional Dirac operators with critical
combinations of electrostatic and Lorentz scalar shell interactions supported by a
compact smooth surface. It turns out that the criticality of the interaction
may result in a new interval of essential spectrum. The position and the
length of the interval are explicitly controlled by the coupling constants
and the principal curvatures of the surface. This effect is completely new
compared to lower-dimensional critical situations or special geometries considered
up to now, in which only a single new point in the essential spectrum was
observed.
Keywords
Dirac operator, pseudodifferential operators, essential
spectrum, principal curvature, transmission condition,
boundary integral operator
