  Because spatio-temporal tensors are associated with the Lorentz group,
whereas spinors are associated with its covering group SL(2, C), one can
associate with every tensor a spinor (but not vice versa). In particular, the
(1,0)+(0,1) representation of SL(2, C) can provide a six-component spinor
equivalent to the electromagnetic field tensor. The chief aim of this work is
to develop the (1,0)+(0,1) description for the electromagnetic field in the
absence of sources, rigorously and systematically, which should be useful if we
are to deal with those issues involving with single-photon states and the
angular momentum of light, etc. Based on our formalism, the quantum theory and
some symmetries of the photon field can be discussed in a new manner, and the
spin-orbit interaction of photons can be described in a form that is closely
analogous to that of the Dirac electron. Moreover, in terms of the (1,0)+(0,1)
description, one can treat the photon field in curved spacetime via spin
connection and the tetrad formalism, which is of great advantage to study the
gravitational spin-orbit coupling of photons.
