Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The relations of the homogeneous Maxwell's equations to the theory of
  functions   The thesis developed by Cornelius Lanczos in his doctoral dissertation is
that electrodynamics is a pure field theory which is hyperanalytic over the
algebra of biquaternions. In this theory Maxwell's homogeneous equations
correspond to a generalization of the Cauchy-Riemann regularity conditions to
four complex variables, and electrons to singularities in the Maxwell field.
Since there are no material particles in Lanczos electrodynamics, the same
action principle applies to both regular and singular Maxwell fields.
Therefore, the usual action integral of classical electrodynamics is {not} an
input in that theory, but rather a consequence which {derives} from the
application of Hamilton's principle to a superposition of two or more
homogeneous Maxwell fields. This leads to a fully consistent electrodynamics
which, moreover, can be shown to be finite. As byproducts to this remarkable
thesis Lanczos anticipated the Moisil-Fueter theory of quaternion-analytic
functions by more than ten years; showed that Maxwell's equations are invariant
in both spin-1 and spin-1/2 Lorentz transformations; that displacing a
singularity into imaginary space adds an intrinsic magnetic-like field to its
electric field; and that his theory does even include gravitation -- although
not in the general relativistic form of Einstein to whom Lanczos dedicated his
dissertation.

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The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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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: patt-sol
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The categories of this paper are: bayes-an