The Dirac equation in an external electromagnetic field: symmetry algebra and exact integration

Abstract

Integration of the Dirac equation with an external electromagnetic field is explored in the framework of the method of separation of variables and of the method of noncommutative integration. We have found a new type of solutions that are not obtained by separation of variables for several external electromagnetic fields. We have considered an example of crossed electric and magnetic fields of a special type for which the Dirac equation admits a nonlocal symmetry operator

References in corpus (4)

• The Casimir effect with quantized charged spinor matter in background magnetic field
• Integrating Klein-Gordon-Fock equations in an external electromagnetic field on Lie groups
• The Casimir effect with quantized charged scalar matter in background magnetic field
• Yang-Mills gauge fields conserving the symmetry algebra of the Dirac equation in a homogeneous space

Cited by in corpus (9)

• Separation of variables in Hamilton-Jacobi equation for a charged test particle in the Stackel spaces of type (2.0)
• Dirac Hamiltonian in a supersymmetric framework
• On the connection between the solutions to the Dirac and Weyl equations and the corresponding electromagnetic 4-potentials
• Energy-driven disorder in the mean field QCD
• Envelope-function theory of inhomogeneous strain in semiconductor nanostructures
• General solution vs spin invariant eigenstates of the Dirac equation with the Coulomb potential
• In- and out-states of scalar particles confined between two capacitor plates
• Noncommutative reduction of the nonlinear Schrödinger equation on Lie groups
• Dirac-like Hamiltonians associated to Schrödinger factorizations