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

DOI10.1142/S0219887818500858zbMath1390.35302arXiv1709.04644WikidataQ126072941 ScholiaQ126072941MaRDI QIDQ4635351

A. I. Breev, Alexander Shapovalov

Publication date: 16 April 2018

Published in: International Journal of Geometric Methods in Modern Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.04644

zbMATH Keywords

separation of variablessymmetry operators\((2 + 1)\)-dimensional Dirac equation

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Linear first-order PDEs (35F05) Symmetries, invariants, etc. in context of PDEs (35B06) Time-dependent Schrödinger equations and Dirac equations (35Q41) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35) PDEs on manifolds (35R01)

Related Items (4)

Algebras of symmetry operators of the Klein-Gordon-Fock equation for groups acting transitively on two-dimensional subspaces of a space-time manifold ⋮ Algebras of integrals of motion for the Hamilton–Jacobi and Klein–Gordon–Fock equations in spacetime with four-parameter groups of motions in the presence of an external electromagnetic field ⋮ Vector triads of homogeneous spaces matched with the Killing fields ⋮ Integration of the Hamilton-Jacobi and Maxwell equations in diagonal metrics of Stäckel spaces

Cites Work

• Unnamed Item
• Unnamed Item
• The Dirac equation and its solutions
• Self-adjoint extensions in quantum mechanics. General theory and applications to Schrödinger and Dirac equations with singular potentials.
• On the orbits in the Lie algebras of some (pseudo) orthogonal groups
• Quantum de Sitter cosmology and phantom matter
• Zero-mass fermions in Coulomb and Aharonov-Bohm potentials in 2+1 dimensions
• Solutions of relativistic wave equations in superpositions of Aharonov–Bohm, magnetic, and electric fields
• Exact solution of Dirac equation in 2+1 dimensional gravity
• New method of integration for the Dirac equation on a curved space-time
• Black hole in three-dimensional spacetime
• Inflationary universe in terms of a van der Waals viscous fluid
• Green functions of the Dirac equation with magnetic-solenoid field

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