Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relativistic vortex electrons: paraxial versus non-paraxial regimes   A plane-wave approximation in particle physics implies that a width of a
massive wave packet $\sigma_{\perp}$ is much larger than its Compton wavelength
$\lambda_c = \hbar/mc$. For Gaussian beams or for packets with the non-singular
phases (say, the Airy beams), corrections to this approximation are attenuated
as $\lambda_c^2/\sigma_{\perp}^2 \ll 1$ and usually negligible. Here we show
that this situation drastically changes for particles with the phase vortices
associated with an orbital angular momentum $\ell\hbar$. For highly twisted
beams with $|\ell| \gg 1$, the non-paraxial corrections get $|\ell|$ times
enhanced and $|\ell|$ can already be as large as $10^3$. We describe the
relativistic wave packets, both for vortex bosons and fermions, which transform
correctly under the Lorentz boosts, are localized in a 3D space, and represent
a non-paraxial generalization of the massive Laguerre-Gaussian beams. We
compare such states with their paraxial counterpart paying specific attention
to the relativistic effects and to the differences from the twisted photons. In
particular, a Gouy phase is found to be Lorentz invariant and it generally
depends on time rather than on a distance $z$. By calculating the electron
packet's mean invariant mass, magnetic moment, etc., we demonstrate that the
non-paraxial corrections can already reach the relative values of $10^{-3}$.
These states and the non-paraxial effects can be relevant for the proper
description of the spin-orbit phenomena in relativistic vortex beams, of
scattering of the focused packets by atomic targets, of collision processes in
particle and nuclear physics, and so forth.

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The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol