Related papers: The relativistic Pauli equation
We derive a general relativistic Hamiltonian valid for both bound and scattering systems by reducing the four-component Dirac equation to a two-component Dirac-Pauli form. Unlike conventional approaches, our formulation includes first-order…
It has long been speculated that the Dirac or, more generally, the Dirac-Pauli spinor in the Foldy-Wouthuysen (FW) representation should behave like a classical relativistic spinor in the low-energy limit when the probability of…
We show that, in the relativistic regime, scalar bosons satisfy a quantum wave equation which is quite analogous to the Dirac equation. In contrast with the Klein-Gordon equation it is first order with respect to time derivation. It leads…
In this paper we represent the generalization of relativistic quantum mechanics on the base of eght-component values "octons", generating associative noncommutative spatial algebra. It is shown that the octonic second-order equation for the…
We study the Dirac equation for spinor wavefunctions minimally coupled to an external field, from the perspective of an algebraic system of linear equations for the vector potential. By analogy with the method in electromagnetism, which has…
We show that spin-flip probabilities emerge in the relativistic regime for scalar potentials, absent in the standard Dirac representation. We examine 1D scattering for the Dirac equation employing an alternate matrix representation…
Starting with the quaternionic Minkowski space-time and its four-vector representation, a rotational analogue of the quaternionic Dirac equation in the electromagnetic field is developed, which includes not only the energy solutions but…
Closed-form, normalizable solutions of Dirac's equation propagating within a semi-infinite cylindrical waveguide are obtained in terms of ordinary and modified Bessel functions. These relativistic wave packets induce quantum backflow on a…
We obtain exact solution of the Dirac equation for a charged particle with position-dependent mass in the Coulomb field. The effective mass of the spinor has a relativistic component which is proportional to the square of the Compton…
The deformed Dirac equation invariant under the $\kappa$-Poincar\'{e}-Hopf quantum algebra in the context of minimal and scalar couplings under spin and pseudospin symmetries limits is considered. The $\kappa$-deformed Pauli-Dirac…
The relativistic approach to electroweak properties of two-particle composite systems developed previously is generalized here to the case of nonzero spin. This approach is based on the instant form of relativistic Hamiltonian dynamics. A…
The behavior of an electron spin interacting with a linearly polarized laser field is analyzed. In contrast to previous considerations of the problem, the initial state of the electron represents a localized wave packet, and a spatial…
We consider different variants of factorization of a 2x2 matrix Schroedinger/Pauli operator in two spatial dimensions. They allow to relate its spectrum to the sum of spectra of two scalar Schroedinger operators, in a manner similar to…
We consider the consistent deformation of the relativistic quantum mechanics introducing the noncommutativity of the space-time and preserving the Lorentz symmetry. The relativistic wave equation describing the spinning particle on…
We derive relativistic equations for charged and neutral spin particles. The approach for higher-spin particles is based on generalizations of the Bargmann-Wigner formalism. Next, we study, what new physical information can the introduction…
We construct all (2+1)-dimensional PDEs depending only on 2nd-order derivatives of unknown which have the Euler-Lagrange form and determine the corresponding Lagrangians. We convert these equations and their Lagrangians to two-component…
Following the Poincare algebra for a free spinning particle and using the Casimirs of the algebra in the Hamiltonian approach, we construct systematically a set of Lagrangians for the relativistic spinning particle which includes the…
This work analyses hadronic decays of exotic mesons, with a focus on the lightest one, the $J^{PC}=1^{-+}$ $\pi_{1}$, in a fully relativistic formalism, and makes comparisons with non-relativistic results. We also discuss Coulomb gauge…
In this paper, we investigate an alternative formulation for spin 3/2 field equation. First we will review equation of motion of Dirac and Maxwell, and then construct the equation for spin 3/2 in the similar fashion. Our method actually a…
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…