Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Radiation by Moving Charges   It is generally accepted that the dynamics of relativistic particles in the
lab frame can be described by taking into account the relativistic dependence
of the particles momenta on the velocity, with no reference to Lorentz
transformations. The electrodynamics problem can then be treated within a
"single inertial frame" description. To evaluate radiation fields from moving
charged particles we need their velocities and positions as a function of the
lab frame time t. The relativistic motion of a particle in the lab frame is
described by Newton's second law corrected for the relativistic dependence of
the particle momentum on the velocity. In all standard derivations the
trajectories in the source part of the usual Maxwell's equations are identified
with the trajectories $\vec{x}(t)$ calculated by using the "corrected" Newton's
second law. This way of coupling fields and particles is considered correct. We
argue that this procedure needs to be changed by demonstrating a
counterintuitive: the results of conventional theory of radiation by
relativistically moving charges are not consistent with the principle of
relativity. The trajectory of a particle in the lab frame consistent with the
usual Maxwell's equations, is found by solving the dynamics equation in
manifestly covariant form, with the proper time $\tau$ used to parameterize the
particle world-line in space-time. We find a difference between the "true"
particle trajectory $\vec{x}(t)$ calculated or measured in the conventional
way, and the covariant particle trajectory $\vec{x}_{cov}(t)$ calculated by
projecting the world-line to the lab frame and using t to parameterize the
trajectory curve. The difference is due to a choice of convention, but only
$\vec{x}_{cov}(t)$ is consistent with the usual Maxwell's equations: therefore,
a correction of the conventional synchrotron-cyclotron radiation theory is
required.

2
The categories of this paper are: math
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org