Local spin base invariance is the extension of the global symmetry the
gamma matrices under similarity transformations to a local symmetry,
decoupling coordinate/Lorentz transformations, thus turning Dirac
spinors to “scalars under Lorentz transformations” in an appropriate
sense. In this talk, I will give a global geometric interpretation of
the local spin base formulation on a curved space-time and in particular
of its central element, the global Dirac structure, in terms of
principal and vector bundles and their endomorphisms. It is shown that
this is intimately related to spin and spin-C-structures in the sense
that the existence of one of those implies the existence of a Dirac
structure and allows an extension to local spin base invariance. Vice
versa, the existence of a Dirac structure implies the existence of a
Spin-C structure. Furthermore, arguments are given that the Dirac
structure is a more natural choice as a variable for (quantum) gravity
than tetrads/vielbeins.