Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Electromagnetic Wavelets as Hertzian Pulsed Beams in Complex Spacetime   Electromagnetic wavelets are a family of 3x3 matrix fields W_z(x')
parameterized by complex spacetime points z=x+iy with y timelike. They are
translates of a \sl basic \rm wavelet W(z) holomorphic in the future-oriented
union T of the forward and backward tubes. Applied to a complex polarization
vector p (representing electric and magnetic dipole moments), W(z) gives an
anti-selfdual solution W(z)p of Maxwell's equations derived from a selfdual
Hertz potential Z(z)=-iS(z)p, where S is the \sl Synge function \rm acting as a
Whittaker-like scalar Hertz potential. Resolutions of unity exist giving
representations of sourceless electromagnetic fields as superpositions of
wavelets. With the choice of a branch cut, S(z) splits into a difference of
retarded and advanced \sl pulsed beams \rm whose limits as y\to 0 give the
propagators of the wave equation. This yields a similar splitting of the
wavelets and leads to their complete physical interpretation as EM pulsed beams
absorbed and emitted by a \sl disk source \rm D(y) representing the branch cut.
The choice of y determines the beam's orientation, collimation and duration,
giving beams as sharp and pulses as short as desired. The sources are computed
as spacetime distributions of electric and magnetic dipoles supported on D(y).
The wavelet representation of sourceless electromagnetic fields now splits into
representations with advanced and retarded sources. These representations are
the electromagnetic counterpart of relativistic coherent-state representations
previously derived for massive Klein-Gordon and Dirac particles.

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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int