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Because spatio-temporal tensors are associated with the Lorentz group,whereas spinors are associated with its covering group SL(2, C), one canassociate 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 spinorequivalent to the electromagnetic field tensor. The chief aim of this work isto develop the (1,0)+(0,1) description for the electromagnetic field in theabsence of sources, rigorously and systematically, which should be useful if weare to deal with those issues involving with single-photon states and theangular momentum of light, etc. Based on our formalism, the quantum theory andsome symmetries of the photon field can be discussed in a new manner, and thespin-orbit interaction of photons can be described in a form that is closelyanalogous 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 spinconnection and the tetrad formalism, which is of great advantage to study thegravitational spin-orbit coupling of photons.

The (1,0)+(0,1) spinor description of the photon field and its preliminary applications