Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Nature of the Vector and Scalar Potentials and Gauge Invariance in
  the Context of Gauge Theory   Modern undergraduate textbooks in electricity and magnetism typically focus
on a force representation of electrodynamics with an emphasis on Maxwell's
Equations and the Lorentz Force Law. The vector potential $\mathbf{A}$ and
scalar potential $\Phi$ play a secondary role mainly as quantities used to
calculate the electric and magnetic fields. However, quantum mechanics
including quantum electrodynamics (QED) and other gauge theories demands a
potential ($\Phi$,$\mathbf{A}$) oriented representation where the potentials
are the more fundamental quantities. Here, we help bridge that gap by showing
that the homogeneous Maxwell's equations together with the Lorentz Force Law
can be derived from assuming that the potentials represent potential energy and
momentum per unit charge. Furthermore, we enumerate the additional assumptions
that are needed to derive the inhomogeneous Maxwell's equations. As part of
this work we demonstrate the physical nature and importance of gauge
invariance.

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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an