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

Abstract

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 (2 + 1)-dimensional Riemann (curved) spacetime. Nonequivalent complete sets of mutually commuting symmetry operators are classified in a (2 + 1)-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.

Original language	English
Article number	1850085
Journal	International Journal of Geometric Methods in Modern Physics
Volume	15
Issue number	5
DOIs	https://doi.org/10.1142/S0219887818500858
Publication status	Published - 1 May 2018

Keywords

(2 + 1)-dimensional Dirac equation
separation of variables
symmetry operators

ASJC Scopus subject areas

Physics and Astronomy (miscellaneous)

Access to Document

10.1142/S0219887818500858

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title = "Symmetry operators and separation of variables in the (2 + 1)-dimensional Dirac equation with external electromagnetic field",

abstract = "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 (2 + 1)-dimensional Riemann (curved) spacetime. Nonequivalent complete sets of mutually commuting symmetry operators are classified in a (2 + 1)-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.",

keywords = "(2 + 1)-dimensional Dirac equation, separation of variables, symmetry operators",

author = "Shapovalov, {A. V.} and Breev, {A. I.}",

year = "2018",

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language = "English",

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N2 - 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 (2 + 1)-dimensional Riemann (curved) spacetime. Nonequivalent complete sets of mutually commuting symmetry operators are classified in a (2 + 1)-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.

AB - 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 (2 + 1)-dimensional Riemann (curved) spacetime. Nonequivalent complete sets of mutually commuting symmetry operators are classified in a (2 + 1)-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.

KW - (2 + 1)-dimensional Dirac equation

KW - separation of variables

KW - symmetry operators

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