  A review of some facts concerning classical spacetime geometry is presented
together with a description of the most elementary aspects of the two-component
spinor formalisms of Infeld and van der Waerden. Special attention is
concentrated upon the gauge characterization of the basic geometric objects
borne by the formalisms. It is pointed out that spin-affine configurations are
most naively defined by carrying out parallel displacements of null world
vectors within the framework of the {\gamma}-formalism. The standard result
that assigns a covariant gauge behaviour to the symmetric parts of any
admissible spin connexions is deduced out of building up a generalized version
of spin transformation laws. A fairly complete algebraic description of
curvature splittings is carried out on the basis of the construction of a set
of spinor commutators for each formalism. The pertinent computations take up
the utilization of some covariant differential prescriptions which facilitate
specifying the action of the commutators on arbitrary spin tensors and
densities. It turns out that the implementation of such commutators under
certain circumstances gives rise to a system of wave equations for gravitons
and Infeld-van der Waerden photons which possess in either formalism a
gauge-invariance property associated with appropriate spinor-index
configurations. The situation regarding the accomplishment of the couplings
between Dirac fields and electromagnetic curvatures is entertained to a
considerable extent.
