Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Novel, first-principles approach to deriving Electromagnetic field
  transformations under oblique Lorentz-Boosts and arbitrary Spatial Rotations   The standard classic special relativistic transformation of the
electromagnetic (EM) field under proper Lorentz transformations is revisited.
As to the pure Lorentz-boosts, popular treatments on EM transformation
contemplate ideal geometries generating special static charge and steady
current distributions and in conjunction, invoke parallel and perpendicular (to
the boost-velocity) components of the fields so engendered; the outcomes
subsequently being suitably generalized. We demonstrate ab initio, the EM field
transformation under arbitrary oblique uniform relative boost velocities from a
broader, rigorous yet remarkably lucid perspective, exploiting the antisymmetry
of the EM-field tensor and symmetry of the general Lorentz-boost transformation
preemptively eliminating the labor of performing complicated matrix
multiplications. Gratifyingly, this instructive exercise manifestly encompasses
time varying fields and yields the transformation relations in a
coordinate-free form. Further, the EM field transformation under proper,
instantaneous 3D rotations is demonstrated to transform as a passive rotation
of the coordinate axes, where the electric and magnetic fields transform
independently as purely electric and magnetic fields, respectively. The present
didactical exercise, amenable to be incorporated in graduate courses on
relativistic electrodynamics, should serve as an excellent illustration on how
powerful symmetry arguments simplify the otherwise tedious calculations while
endowing complete generality to the connections obtained.

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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph