Dirac-like wave equation for massless particles using the 2+2 decomposition of spacetime

Here we derive a wave equation for massless particles using the 2+2 decomposition of spacetime. The generators of the symmetry group, whose representation these massless particles belong, is constructed using the null vectors from the decomposition. A possible application of this formalism to the problem of finding a photon wave function is explored; if valid, this formalism could be an alternative to gauge theories.