Related papers: Photonic realization of the kappa-deformed Dirac e…
We consider systems described by the two-dimensional Dirac equation where the Fermi velocity is inhomogeneous as a consequence of mechanical deformations. We show that the mechanical deformations can lead to deflection and focusing of the…
We consider quantum rings realized in materials where the dynamics of charge carriers mimics that of two-dimensional (2D) Dirac electrons. A general theoretical description of the ring-subband structure is developed that applies to a range…
In a Minkowski spacetime, one may transform the Dirac wave function under the spin group, as one transforms coordinates under the Poincar\'e group. This is not an option in a curved spacetime. Therefore, in the equation proposed…
The properties of the equation of Dirac type in three-dimensional and five-dimensional Minkowski space-time with respect to time reflection (in sense of Pauli and Wigner) as well as to the operation of charge conjugation are investigated.…
We show that the Dirac equation can be rewritten as a relation describing the fundamental symmetry group of special topological manifold corresponding to the Dirac wave field. It leads to unification of the time-space and internal…
In this paper, we derive corrections to the geodesic equation due to the $k$-deformation of curved space-time, up to the first order in the deformation parameter a. This is done by generalizing the method from our previous paper [31], to…
Similar to the optical diffraction of light passing through a material grating, the Kapitza-Dirac effect occurs when an electron is diffracted by a standing light wave. In its original description the effect is time-independent. In the…
Elastic wave propagation is a century-old problem. Unlike on a flat manifold, analytical solution is not well established for a curved manifold. In this study we take a step towards building an analytical framework for solving the elastic…
The impact of light scalars coupled conformally and disformally to matter on the geodetic and frame-dragging (FD) precessions is calculated. For larger frequencies the disformal interaction becomes increasingly relevant. We use several…
We investigate a particle velocity in the $\kappa$-Minkowski space-time, which is one of the realization of a noncommutative space-time. We emphasize that arrival time analyses by high-energy $\gamma$-rays or neutrinos, which have been…
We present the alternative way of derivation of the Wandzura-Wilczek relations between the kinematical twist-3 and twist-2 functions, parameterizing hadronic matrix element in two-photon processes $\gamma^{\star}\pi\to \gamma\pi$ and…
In this paper we revisit the model of $\kappa$-deformed complex scalar field. We find that this model possesses ten conserved Noether charges that form, under commutators, a representation of (undeformed) Poincar\'e algebra. It follows that…
The Dirac equation is a cornerstone in the history of physics, merging successfully quantum mechanics with special relativity, providing a natural description of the electron spin and predicting the existence of anti-matter. Furthermore, it…
We present a spectral triple for $\kappa$-Minkowski space in two dimensions. Starting from an algebra naturally associated to this space, a Hilbert space is built using a weight which is invariant under the $\kappa$-Poincar\'e algebra. The…
The dynamics of low energy electrons in general static strained graphene surface is modelled mathematically by the Dirac equation in curved space-time. In Cartesian coordinates, a parametrization of the surface can be straightforwardly…
We show how a deformed composition law of four-momenta can be used to define, at the classical level, a modified notion of spacetime for a system of two particles through the crossing of worldlines in particle interactions. We present a…
We show a procedure to classically simulate the Majorana equation in 1+1 dimensions via two one-dimensional photonic crystals. We use a decomposition of the Majorana equation into two Dirac equations and propose a novel approach that uses a…
In the present article we show that the energy spectrum of the one-dimensional Dirac equation, in the presence of an attractive vectorial delta potential, exhibits a resonant behavior when one includes an asymptotically spatially vanishing…
We have proposed a generally covariant non-relativistic particle model that can represent the $\kappa$-Minkowski noncommutative spacetime. The idea is similar in spirit to the noncommutative particle coordinates in the lowest Landau level.…
The motion of a relativistic particle is linked to its spin by the Dirac equation. Remarkably, electrons in two-dimensional materials can mimic such Dirac particles but must always appear in pairs of opposite spin chirality. Using…