The most general combination of couplings of fermions with external potentials in 1+1 dimensions, must include vector, scalar and pseudoscalar potentials. We consider such a mixing of potentials in a PT-symmetric time-independent Dirac equation. The Dirac equation is mapped into an effective PT-symmetric Schrödinger equation. Despite the non-hermiticity of the effective potential, we find real ...

In a three-dimensional bounded possibly multiply connected domain, we prove the existence, uniqueness, and regularity of some vector potentials, associated with divergence-free function satis...

We review the status of quasi-degenerate doublets in nuclei, called pseudospin doublets, which were discovered about thirty years ago and the origins of which have remained a mystery, until recently. We show that pseudospin doublets originate from an SU(2) symmetry of the Dirac Hamiltonian which occurs when the sum of the scalar and vector potentials is a constant. Furthermore, we survey the ev...

Atomic nuclei exhibit approximate pseudospin symmetry. We review the arguments that this symmetry is a relativistic symmetry. The condition for this symmetry is that the sum of the vector and scalar potentials in the Dirac Hamiltonian is a constant. We give the generators of pseudospin symmetry. We review some of the predictions that follow from the insight that pseudospin symmetry has relativi...

We review the status of a quasi degenerate doublets in nuclei, called pseudospin doublets, which were discovered about thirty years ago and the origins of which have remained a mystery, until recently. We show that pseudospin doublets originate from an SU(2) symmetry of the Dirac Hamiltonian which occurs when the scalar and vector potentials are opposite in sign but equal in magnitude. Furtherm...

We prove the Anderson localization near the bottom of the spectrum for two dimensional discrete Schrödinger operators with a class of random vector potentials and no scalar potentials. Main lemmas are the Lifshitz tail and the Wegner estimate on the integrated density of states. Then, the Anderson localization, i.e., the pure point spectrum with exponentially decreasing eigenfunctions, is prove...