Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solutions of the Maxwell equations and photon wave functions   Properties of six-component electromagnetic field solutions of a matrix form
of the Maxwell equations, analogous to the four-component solutions of the
Dirac equation, are described. It is shown that the six-component equation,
including sources, is invariant under Lorentz transformations. Complete sets of
eigenfunctions of the Hamiltonian for the electromagnetic fields, which may be
interpreted as photon wave functions, are given both for plane waves and for
angular-momentum eigenstates. Rotationally invariant projection operators are
used to identify transverse or longitudinal electric and magnetic fields. For
plane waves, the velocity transformed transverse wave functions are also
transverse, and the velocity transformed longitudinal wave functions include
both longitudinal and transverse components. A suitable sum over these
eigenfunctions provides a Green function for the matrix Maxwell equation, which
can be expressed in the same covariant form as the Green function for the Dirac
equation. Radiation from a dipole source and from a Dirac atomic transition
current are calculated to illustrate applications of the Maxwell Green
function.

20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ