A system of a single relativistic electron interacting with the quantized electromagnetic field is considered. We mainly study this system with a fixed total momentum p — This system is called the Dirac polaron. We analyze the lowest energyE(p) of the Dirac polaron, and derive some properties: concavity, symmetricity, and the inverse energy inequality E(p) ≤ E(0), p ∈ R. Furthermore, we conside...

The approximate analytical solutions of the Dirac equations with the reflectionless-type and Rosen-Morse potentials including the spin-orbit centrifugal (pseudo-centrifugal) term are obtained. Under the conditions of spin and pseudospin (pspin) symmetry concept, we obtain the bound state energy spectra and the corresponding two-component upperand lower-spinors of the two Dirac particles by mean...

Neutrinos may be pseudo-Dirac states, such that each generation is actually composed of two maximally mixed Majorana neutrinos separated by a tiny mass difference. The usual active neutrino oscillation phenomenology would be unaltered if the pseudo-Dirac splittings are deltam(2) less, similar 10(-12) eV(2); in addition, neutrinoless double beta decay would be highly suppressed. However, it may ...

We investigate the convergence properties of a three-dimensional quantum lattice Boltzmann scheme for the Dirac equation. These schemes were constructed as discretizations of the Dirac equation based on operator splitting to separate the streaming along the three coordinate axes, but their output has previously only been compared against solutions of the Schrödinger equation. The Schrödinger eq...

The fractal spectrum of magnetic minibands (Hofstadter butterfly), induced by the moiré superlattice of graphene on a hexagonal crystal substrate, is known to exhibit gapped Dirac cones. We show that the gap can be closed by slightly misaligning the substrate, producing a hierarchy of conical singularities (Dirac points) in the band structure at rational values Φ = (p/q)(h/e) of the magnetic fl...

The Dirac equation is expressed entirely in terms of geometrical quantities by providing a geometrical interpretation for the (−1) which appears explicitly in the Dirac equation. In the modification of the Dirac electron theory which ensues, the (−1) appears as the generator of rotations in the spacelike plane orthogonal to the plane containing the electron current and spin vectors. This amount...

Dirac structures appear naturally in the study of certain classes of physical models described by partial differential equations (p.d.e.’s). They are the underlying power conserving structures of the p.d.e.’s. We study these structures and their properties from an operator-theoretic point of view. In particular, we find necessary and sufficient conditions for the composition of two Dirac struct...

The Coulomb interaction among massless Dirac fermions in graphene is unscreened around the isotropic Dirac points, causing a logarithmic velocity renormalization and a cone reshaping. In less symmetric Dirac materials possessing anisotropic cones with tilted axes, the Coulomb interaction can provide still more exotic phenomena, which have not been experimentally unveiled yet. Here, using site-s...

For the description of space-time fermions, Dirac-Kähler fields (inhomogeneous differential forms) provide an interesting alternative to the Dirac spinor fields. In this paper we develop a similar concept within the symplectic geometry of phase-spaces. Rather than on space-time, symplectic Dirac-Kähler fields can be defined on the classical phasespace of any Hamiltonian system. They are equival...

We are familiar with Dirac equation in flat space by which we can investigate the behaviour of half-integral spin particle. With the introduction of general relativistic effects the form of the Dirac equation will be modified. For the cases of different background geometry like Kerr, Schwarzschild etc. the corresponding form of the Dirac equation as well as the solution will be different. In 19...