Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conservation of reactive electromagnetic energy in reactive time   The complex Poynting theorem (CPT) is extended to a canonical time-scale
domain $(t,s)$. Time-harmonic phasors are replaced by the positive-frequency
parts of general fields, which extend analytically to complex time $t+is$, with
$s>0$ interpreted as a time resolution scale. The real part of the extended CPT
gives conservation in $t$ of a time-averaged field energy, and its imaginary
part gives conservation in $s$ of a time-averaged reactive energy. In both
cases, the averaging windows are determined by a Cauchy kernel of width $\Delta
t\sim \pm s$. This completes the time-harmonic CPT, whose imaginary part is
generally supposed to be vaguely `related to' reactive energy without giving a
conservation law, or even an expression, for the latter. The interpretation of
$s$ as reactive time, tracking the leads and lags associated with stored
capacitative and inductive energy, gives a simple explanation of the
volt-ampere reactive (var) unit measuring reactive power: a var is simply one
Joule per reactive second. The related 'complex radiation impedance density' is
introduced to represent the field's local reluctance to radiate.

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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
1
The categories of this paper are: cs
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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: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg