Anomalous relativistic tunneling and exotic point interactions

We examine the one-dimensional quantum scattering of a Dirac particle off relativistic potential barriers. With proper considerations of the Dirac sea, the existence of anomalous tunneling at zero incident energy is revealed for a particular type of relativistic potential having the same magnitudes and opposite signs for scalar and vector components. It is also shown that this leads to an exotic short-range limit of the potentials.