Corrigendum to “Solution of the Dirac equation by separation of variables in spherical coordinates for a large class of noncentral electromagnetic potentials” [Ann. Phys. 320 (2005) 453–467]

2006 ◽  
Vol 321 (6) ◽  
pp. 1524-1525
Author(s):  
A.D. Alhaidari
Keyword(s):  
Dirac Equation ◽  
Large Class ◽  
Separation Of Variables ◽  
Spherical Coordinates ◽  
Electromagnetic Potentials

scholarly journals Non-Commutative Integration of the Dirac Equation in Homogeneous Spaces

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1867
Author(s):  
Alexander Breev ◽  
Alexander Shapovalov
Keyword(s):  
Dirac Equation ◽  
Exact Solutions ◽  
Homogeneous Space ◽  
Integration Method ◽  
Homogeneous Spaces ◽  
Separation Of Variables ◽  
General Structure ◽  
Three Dimensional ◽  
De Sitter ◽  
Elementary Functions

We develop a non-commutative integration method for the Dirac equation in homogeneous spaces. The Dirac equation with an invariant metric is shown to be equivalent to a system of equations on a Lie group of transformations of a homogeneous space. This allows us to effectively apply the non-commutative integration method of linear partial differential equations on Lie groups. This method differs from the well-known method of separation of variables and to some extent can often supplement it. The general structure of the method developed is illustrated with an example of a homogeneous space which does not admit separation of variables in the Dirac equation. However, the basis of exact solutions to the Dirac equation is constructed explicitly by the non-commutative integration method. In addition, we construct a complete set of new exact solutions to the Dirac equation in the three-dimensional de Sitter space-time AdS3 using the method developed. The solutions obtained are found in terms of elementary functions, which is characteristic of the non-commutative integration method.

scholarly journals Symmetry operators and separation of variables in the (2 + 1)-dimensional Dirac equation with external electromagnetic field

2018 ◽  
Vol 15 (05) ◽  
pp. 1850085 ◽  
Author(s):  
A. V. Shapovalov ◽  
A. I. Breev
Keyword(s):  
Dirac Equation ◽  
Separation Of Variables ◽  
Flat Space ◽  
External Electromagnetic Field ◽  
Complete Separation ◽  
Electromagnetic Potential ◽  
First Order ◽  
Matrix Coefficients ◽  
Symmetry Operators ◽  
Differential Symmetry

We obtain and analyze equations determining first-order differential symmetry operators with matrix coefficients for the Dirac equation with an external electromagnetic potential in a [Formula: see text]-dimensional Riemann (curved) spacetime. Nonequivalent complete sets of mutually commuting symmetry operators are classified in a [Formula: see text]-dimensional Minkowski (flat) space. For each of the sets, we carry out a complete separation of variables in the Dirac equation and find a corresponding electromagnetic potential permitting separation of variables.

Matrix operator symmetries of the Dirac equation and separation of variables

1986 ◽  
Vol 27 (7) ◽  
pp. 1893-1900 ◽  
Author(s):  
E. G. Kalnins ◽  
W. Miller ◽  
G. C. Williams
Keyword(s):  
Dirac Equation ◽  
Separation Of Variables ◽  
Matrix Operator

scholarly journals THE DIRAC PARTICLE ON CENTRAL BACKGROUNDS AND THE ANTI-DE SITTER OSCILLATOR

1998 ◽  
Vol 13 (36) ◽  
pp. 2923-2935 ◽  
Author(s):  
ION. COTĂESCU
Keyword(s):  
Dirac Equation ◽  
Special Relativity ◽  
Scalar Product ◽  
Energy Levels ◽  
Specific Form ◽  
Dirac Particle ◽  
Spherically Symmetric ◽  
Spherical Coordinates ◽  
De Sitter

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 that the spherical coordinates can be separated in terms of angular spinors like in special relativity, obtaining a pair of radial equations and a specific form of the radial scalar product. As an example, we analytically solve the anti-de Sitter oscillator giving the formula of the energy levels and the form of the corresponding eigenspinors.

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