Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Renormalization in Lorentz-Abraham-Dirac Equation, Describing Radiation
  Force in Classical Electrodynamics (in Russian)   While he derived the equation for the radiation force, Dirac (1938) mentioned
a possibility to use different choices for the 4-momentum of an emitting
electron. Particularly, the 4-momentum could be non-colinear to the electron
4-velocity. This ambiguity in the electron 4-momentum allows us to assume that
the mass of emitting electron may be an operator, or, at least, a 4-tensor
instead of being the usually assumed scalar, which relates the 4-velocity of a
bare charge to the total momentum of a dressed point electron, the latter being
a total of the momentum of the bare electron and that of the own
electromagnetic field.
  On applying the re-normalization procedure to the mass operator, we arrive at
an interesting dichotomy. The first choice (more close to traditional one)
ensures the radiation force to be orthogonal to the 4-velocity. In this way the
re-normalization results in the Lorentz-Abraham-Dirac equation or in the
Eliezer equation. However, the 4-momentum of electron in this case is not well
defined: the equality in the relativistic entity (E/c)^2=m^2c^2+p^2 appears to
be broken and even the energy is not definite positive. The latter is an
underlying reason for the 'run-away' solution.
  The other choice is to require the radiation force to be orthogonal to the
4-momentum (not to the 4-velocity). In this case the energy and momentum are
well-defined and obey the relationship (E/c)^2=m^2c^2+p^2. Remarkably, the
equations of a particle's motion in this case differ significantly from all the
known versions. They appear to be well founded. They are simple, easy to solve,
and can be applied to simulate the particle motion in the focus of an
ultra-bright laser.

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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: q-alg