  Thomas-Whitehead (TW) gravity is a gauge theory of gravitation based on
projective geometry. The theory maintains projective symmetry through the TW
connection, an affine connection over the volume bundle of the spacetime
manifold. TW gravity obtains dynamics through Lovelock expansions in the action
while preserving general relativity as a weak field limit. In this paper we
clarify the process of lifting tensor and spinor fields from spacetime to the
volume bundle and demonstrate that a choice of lifting amounts to a gauge
fixing condition. This leads to a natural extension of previous work, where we
now realize these prior constructions have been restricted to a particular
gauge. In pursuit of generality, we also introduce torsion to the TW
connection, leading to new dynamics. In particular, the appearance of torsion
induces interaction terms involving gravitational coupling with Yang-Mills
fields and Dirac spinors. An explicit realization of this is a geometrically
sourced chiral mass term arising from the torsion dynamics.
