The phase factor η η c can be given a geometric interpretation. It has been noted that, for massive Dirac spinors, the "arbitrary" phase factor η η c may depend on both the momentum, and the helicity (but not the chirality). This can be interpreted as saying that this phase may vary along the fiber of the spinor bundle, depending on the local choice of a coordinate frame. Put another way, a spinor field is a local section of the spinor bundle, and Lorentz boosts and rotations correspond to movements along the fibers of the corresponding frame bundle (again, just a choice of local coordinate frame). Examined in this way, this extra phase freedom can be interpreted as the phase arising from the electromagnetic field. For the Majorana spinors, the phase would be constrained to not vary under boosts and rotations.