Gravitational interaction of hadrons and leptons: Linear (multiplicity-free) bandor and nonlinear spinor unitary irreducible representations of S̄L̄ (4 R )

We review two possible affine extensions of gravity connected to the strong interactions. In the metric affine theory, torsion and nonmetricity do not propagate, gravitation is effectively unmodified, and the observed approximate conservation of hadron intrinsic hypermomentum—i.e., scaling,SU (6), and Regge trajectories—is due to theḠL̄ (4,R ) band-spinor structure of the hadrons. In the second approach, the new gravitational Lagrangian density generates propagating but confined torsion and nonmetricity, presumably the main contributions to quark confinement. Leptons are represented nonlinearly as Poincaré spinors with the metric field as “realizer” and Higgs boson, and are unconfined. We present a construction for all linear multiplicity-free (= bandor) representations ofḠL̄ (4,R ) and in particular the [Formula: see text] fitting the hadron manifield. We also construct the Hilbert space hadron states [irreps (irreducible representations) ofḠĀ (4,R )] and the nonlinear realizations ofḠL̄ (4,R ) for lepton fields.