12 research outputs found
General -shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation
In this work we consider the two-dimensional Dirac operator with general
local singular interactions supported on a closed curve. A systematic study of
the interaction is performed by decomposing it into a linear combination of
four elementary interactions: electrostatic, Lorentz scalar, magnetic, and a
fourth one which can be absorbed by using unitary transformations. We address
the self-adjointness and the spectral description of the underlying Dirac
operator, and moreover we describe its approximation by Dirac operators with
regular potentials
Non-self-adjoint relativistic point interaction in one dimension
The one-dimensional Dirac operator with a singular interaction term which is
formally given by , where is an
arbitrary matrix and stands for the Dirac distribution,
is introduced as a closed not necessarily self-adjoint operator. We study its
spectral properties, find its non-relativistic limit and also address the
question of regular approximations. In particular, we show that, contrary to
the case of local approximations, for non-local approximating potentials,
coupling constants are not renormalized in the limit