相关论文: Polar decomposition of a Dirac spinor

The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is discussed. For weak magnetic fields, the approximate energy values are obtained by semiclassical method. In the case with strong…

We reveal that Majorana bound states inside the vortex core in an odd-parity topological superconductivity classified as "pseudo-scalar" type in the gap function are distinctly spin-polarized by solving the massive Dirac Bogoliubov-de…

We investigate whether the spinor field can be differential-algebraically eliminated from the Maxwell--Dirac equations in a particular gauge. To this end, we construct a generic truncated power-series solution and linearize the prolonged…

We consider the Dirac equation written in polar form, without any external potential but equipped with a non-zero tensorial connection, and we find a new type of solution that is localized around the origin with a decreasing exponential…

I describe here the attempt to introduce spin-charge separation in Schrodinger equation. The construction we present here gives a decomposed Schrodinger spinor that has one problem: Its absolute value can only have value between 0 and…

The most general Dirac Hamiltonians in $(1+1)$ dimensions are revisited under the requirement to exhibit a supersymmetric structure. It is found that supersymmetry allows either for a scalar or a pseudo-scalar potential. Their spectral…

Topological semimetals, representing a new topological phase that lacks a full bandgap in bulk states and exhibiting nontrivial topological orders, recently have been extended to photonic systems, predominantly in photonic crystals and to a…

This paper discusses a framework to parametrize and decompose operator matrix elements for particles with higher spin $(j > 1/2)$ using chiral representations of the Lorentz group, i.e. the $(j,0)$ and $(0,j)$ representations and their…

By using symmetry properties, the two-body Dirac equation in coordinate representation is reduced to the coupled pair of radial second-order differential equations. Then the large-j expansion technique is used to solve a bound state…

We explore analytical aspects of correlators involving Dirac spinors in $d+1$- dimensional de Sitter space. Adapting the formalism of Sleight and Taronna, we show how to relate processes involving fermions in the in-in formalism to…

By using two-component approach to the one-dimensional effective mass Dirac equation bound states are investigated under the effect of two new non-PT-symmetric, and non-Hermitian, exponential type potentials. It is observed that the Dirac…

For a spin-1/2 particle moving in a background magnetic field in noncommutative phase space, Dirac equation is solved when the particle is allowed to move off the plane that the magnetic field is perpendicular to. It is shown that the…

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…

Dirac equation for a charged spinor in electromagnetic field is written for special cases of spherically symmetric potentials. This facilitates the introduction of relativistic extensions of shape invariant potential classes. We obtain the…

In the first part of the paper we give a tensor version of the Dirac equation. In the second part we formulate and analyse a simple model equation which for weak external fields appears to have properties similar to those of the…

We present a new approach to study (1+1)-dimensional Dirac equation in the background of an effective mass $M$ by exploiting the possibility of a position-dependent fermi velocity $v_f$. We explore the resulting structure of the coupled…

We rewrite the standard 4-dimensional Dirac equation in terms of quaternionic 2-component spinors, leading to a formalism which treats both massive and massless particles on an equal footing. The resulting unified description has the…

Contemporary presentation of the version 1 demonstrates briefly the development of our investigations and our future goals. The improved free of difficulties in interpretation and printing errors version is presented. The 256-dimensional…

The Dirac equation is not semisimple. We therefore regard it as a contraction of a simpler decontracted theory. The decontracted theory is necessarily purely algebraic and non-local. In one simple model the algebra is a Clifford algebra…

We introduce a new equation we dubbed the modular Dirac equation to see and reconstruct a spin 1/2 particle at the center of a nearly $AdS_2$ spacetime in the entanglement wedge reconstruction paradigm and we study hidden symmetries of this…