Related papers: Spinors and Rodrigues representations associated w…
A system of multiple spacelike separated Dirac particles is considered and a method for constructing polynomial invariants under the spinor representations of the local proper orthochronous Lorentz groups is described. The method is a…
We formulate Lorentz group representations in which ordinary complex numbers are replaced by linear functions of real quaternions and introduce dotted and undotted quaternionic one-dimensional spinors. To extend to parity the space-time…
It is shown the central field Dirac equation can be simplified through the use of real conjugate spinors to substitute for the upper and lower components of the bi-spinor eigensolutions. This substitution reduces the Dirac equation for the…
In this paper we consider the Dirac spinor field in interaction with a background of electrodynamics and torsion-gravity; by performing the polar reduction we acquire the possibility to introduce a new set of objects that have the…
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…
The matrix-valued spherical functions for the pair (K x K, K), K=SU(2), are studied. By restriction to the subgroup A the matrix-valued spherical functions are diagonal. For suitable set of representations we take these diagonals into a…
We introduce a new class of polynomials of multiple orthogonality with respect to the product of $r$ classical discrete weights on integer lattices with noninteger shifts. We give explicit representations in the form of the Rodrigues…
We use variable transformation from the real line to finite or semi-infinite spaces where we expand the regular solution of the 1D time-independent Schrodinger equation in terms of square integrable bases. We also require that the basis…
The supersymmetric analysis of spinning cosmic string spacetime, involving an electron in magnetic fields, has been conducted. We examined the Dirac system within extended special functions known as exceptional orthogonal polynomials.…
The representations of the Schr\"odinger group in one space dimension are explicitly constructed in the basis of the harmonic oscillator states. These representations are seen to involve matrix orthogonal polynomials in a discrete variable…
It is shown that, for spherically symmetric static backgrounds, a simple reduced Dirac equation can be obtained by using the Cartesian tetrad gauge in Cartesian holonomic coordinates. This equation is manifestly covariant under rotations so…
We analyze in detail the analytical solutions of the Dirac equation with scalar S and vector V Coulomb radial potentials near the limit of spin and pseudospin symmetries, i.e., when those potentials have the same magnitude and either the…
In this chapter are given necessary and sufficient conditions for the regularity of solutions of the functional equation appearing in the theory of classical orthogonal polynomials. In addition, we also present the functional Rodrigues…
We show that the Dirac equation for real spinors can be naturally decomposed into a system of two first-order relativistic wave equations. The decomposition separates in a transparent way the real and imaginary parts of the Dirac equation…
The equations for various spin particles with oscillator-like interactions are discussed in this talk. Contents: 1. Comment on "The Klein-Gordon Oscillator"; 2. The Dirac oscillator in quaternion form; 3. The Dirac-Dowker oscillator; 4. The…
We develop a spinor equation of the electromagnetic field, which is equivalent to the Maxwell equation and has a similar form as the Dirac equation. The spinor is the very conjugate momentum of the vector potential in the Lagrangian…
A new classical 2-spinor approach to $U(1)$ gauge theory is presented in which the usual four-potential vector field is replaced by a symmetric second rank spinor. Following a lagrangian formulation, it is shown that the four-rank spinor…
Zeilberger's algorithm provides a method to compute recurrence and differential equations from given hypergeometric series representations, and an adaption of Almquist and Zeilberger computes recurrence and differential equations for…
In this paper, we solve the eigen solutions to some nonlinear spinor equations, and compute several functions reflecting their characteristics. The numerical results show that, the nonlinear spinor equation has only finite meaningful eigen…
Previously (A. Akhmeteli, J. Math. Phys., v. 52, p. 082303 (2011)), the Dirac equation in an arbitrary electromagnetic field was shown to be generally equivalent to a fourth-order equation for just one component of the four-component Dirac…