Electric Quadrupole Moment and the Tensor Magnetic Polarizability of Twisted Electrons and a Potential for their Measurements.

For a twisted (vortex) Dirac particle in nonuniform electric and magnetic fields, the relativistic Foldy-Wouthuysen Hamiltonian is derived including high order terms describing new effects. The result obtained shows for the first time that a twisted spin-1/2 particle possesses a tensor magnetic polarizability and a measurable (spectroscopic) electric quadrupole moment. We have calculated the former parameter and have evaluated the latter one for a twisted electron.

Relativistic Quantum Dynamics of Twisted Electron Beams in Arbitrary Electric and Magnetic Fields.

Relativistic quantum dynamics of twisted (vortex) Dirac particles in arbitrary electric and magnetic fields are constructed for the first time. This allows us to change the controversial contemporary situation when the nonrelativistic approximation is used for relativistic twisted electrons. The relativistic Hamiltonian and equations of motion in the Foldy-Wouthuysen representation are derived.

Manipulating Twisted Electron Beams.

A theoretical description of twisted (vortex) electrons interacting with electric and magnetic fields is presented, based on Lorentz transformations. The general dynamical equations of motion of a twisted electron with an intrinsic orbital angular momentum in an external field are derived. Methods for the extraction of an electron vortex beam with a given orbital polarization and for the manipulation of such a beam are developed.