On the General Projective Theory of Matter and Gravitation

Michael Connolly

A torsional generalization of Thomas-Whitehead (TW) projective connections is proposed. As motivation, the novel projective symmetric teleparallel connection is derived. A projective gauge connection is then introduced and the nonlinear realization technique utilized. The fundamental projective vector of TW theory is extended to a projective generalized Higgs field (pGFH), and used to define a projective 2-frame. The projective Pontrjagin form is then constructed and shown to contain a metric-independent generalization of the Nieh-Yan form. In the gravitational sector, a Lovelock theory coupled to the pGHF is constructed. This is found to provide a rigid pGHF, and a cosmological constant with a contribution from the projective Schouten form. In the matter sector, projective gamma matrices are defined and used to show that spinors require a projective weight, with real part fixed by a projective spinor metric. An extended Dirac operator is formed, leading to a Hermitian, gauge- and coordinate-invariant (massless) action. It is found that Hermiticity does not support interactions with the projective Schouten trace. The field equations are shown to contain a coupling to the distortion tensor, and an induced chiral mass proportional to the undetermined complex projective weight.

To join this event virtually via ZOOM, go to https://uiowa.zoom.us/j/99570315915.