Quantum charged spinning massless particles in 2 + 1 dimensions

Motivated by the conduction properties of graphene discovered and studied in the last decades, we consider the quantum dynamics of a massless, charged, spin 1/2 relativistic particle in three dimensional space-time, in the presence of an electrostatic field in various configurations such as step or barrier potentials and generalizations of them. The field is taken as parallel to the y coordinate axis and vanishing outside of a band parallel to the x axis. The classical theory is reviewed, together with its canonical quantization leading to the Dirac equation for a 2-component spinor. Stationary solutions are numerically found for each of the field configurations considered, from which we calculate the mean quantum trajectories of the particle and compare them with the corresponding classical trajectories, the latter showing a classical version of the Klein phenomenon. Transmission and reflection probabilities are also calculated, confirming the Klein phenomenon.

A local description of dark energy in terms of classical two-component massive spin-one uncharged fields on spacetimes with torsionful affinities

It is assumed that the two-component spinor formalisms for curved spacetimes that are endowed with torsionful affine connexions can supply a local description of dark energy in terms of classical massive spin-one uncharged fields. The relevant wave functions are related to torsional affine potentials which bear invariance under the action of the generalized Weyl gauge group. Such potentials are thus taken to carry an observable character and emerge from contracted spin affinities whose patterns are chosen in a suitable way. New covariant calculational techniques are then developed towards deriving explicitly the wave equations that supposedly control the propagation in spacetime of the dark energy background. What immediately comes out of this derivation is a presumably natural display of interactions between the fields and both spin torsion and curvatures. The physical properties that may arise directly fromthe solutions to thewave equations are not brought out.

Relativistic symmetries of fermions in the background of the inversely quadratic Yukawa potential with Yukawa potential as a tensor

In the presence of spin and pseudo-spin symmetries, we obtain approximate analytical bound state solutions to the Dirac equation with scalar–vector inverse quadratic Yukawa potential including a Yukawa tensor interaction for any arbitrary spin–orbit quantum number, κ. The energy eigenvalues and their corresponding two-component spinor wave functions are obtained in closed form using the parametric Nikiforov–Uvarov method. It is noticed that the tensor interaction removes the degeneracy in the spin and p-spin doublets. Some numerical results are obtained for the lowest energy states within spin and pseudo-spin symmetries.

OBLIQUE CORRECTIONS IN THE MSSM AT ONE LOOP II: FERMIONS

This paper is the completion of an earlier work arXiv:1207.4867 which involves the derivation of oblique corrections in the MSSM at one-loop. In terms of the two-component spinor formalism, which is new in comparison with those used in the literature, the contributions arising from the fermion superpartners, i.e. neutralino-chargino sector to self-energy of Standard Model electroweak gauge bosons are calculated. Corresponding descendants the S, T and U parameters are presented. The validity of our results is examined in two ways, which are then followed by detailed analysis on the results in the literature.

THE FLAVOR SYMMETRY IN THE STANDARD MODEL AND THE TRIALITY SYMMETRY

A Dirac fermion is expressed by a four-component spinor, which is a combination of two quaternions and can be treated as an octonion. The octonion possesses the triality symmetry, which defines symmetry of fermion spinors and bosonic vector fields. The triality symmetry relates three sets of spinors and two sets of vectors, which are transformed among themselves via transformations G23, G12, G13, G123 and G132. If the electromagnetic (EM) interaction is sensitive to the triality symmetry, i.e. EM probe selects one triality sector, EM signals from the five transformed world would not be detected and be treated as the dark matter. According to an astrophysical measurement, the ratio of the dark to ordinary matter in the universe as a whole is almost exactly 5. We expect quarks are insensitive to the triality, and triality will appear as three times larger flavor degrees of freedom in the lattice simulation.

On the Majorana Equation: Relations between Its Complex Two-Component and Real Four-Component Eigenfunctions

We first derive without recourse to the Dirac equation the two-component Majorana equation with a mass term by a direct linearization of the relativistic dispersion relation of a massive particle. Thereby, we make only use of the complex conjugation operator and the Pauli spin matrices, corresponding to the irreducible representation of the Lorentz group. Then we derive the complex two-component eigenfunctions of the Majorana equation and the related quantum fields in a concise way, by exploiting the so-called chirality conjugation operator that involves the spin-flip operator. Subsequently, the four-component spinor solutions of the real Majorana equation are derived, and their intrinsic relations with the spinors of the complex two-component version of the Majorana equation are revealed and discussed extensively.