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

Abstract

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 the ḠL̄ (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 of ḠL̄ (4, R ) and in particular the [Formula: see text] fitting the hadron manifield. We also construct the Hilbert space hadron states [irreps (irreducible representations) of ḠĀ (4, R )] and the nonlinear realizations of ḠL̄ (4, R ) for lepton fields.

Fundamental Symmetries and Spacetime Geometries in Gauge Theories of Gravity—Prospects for Unified Field Theories

“…Note that in this model the connection is non-Lorentzian and the non-metricity 1-form (represented by Q) is non-vanishing. The bosonic sector of metric-affine gravity was analyzed, for instance, in References [62][63][64][65], while the fermionic part is more delicate (see for instance References [66][67][68][69]). In this respect, there is no finite dimensional spinor representation of the GL(4, ) group, which leads to the introduction of the "world spinors" (with infinite components) of Ne'eman, and to the corresponding generalization of Dirac equation.…”

D = 4 topological gravity from gauging the Maxwell-special-affine group

“…So there are widespread usage areas for affine symmetry from particle physics to gravitation [10,12,14,23,[54][55][56][57]. For instance, according to the papers [10][11][12][13][14][15], the gauge theory of affine group could play an important role for solving the renormalizability or unitarity problems on quantum gravity by means of the general linear connection which contains additional degrees of freedom. Also, the paper [58] demonstrated that the pure affine field theory developed by Einstein [59] and Schrödinger [60], known as the Einstein-Schrödinger theory, provides the unification of quantum theory and Einstein's general theory of relativity and this theory can be quantized by the rules of canonical quantization, but the author says that this quantization is physically meaningless.…”

“…Another study, named as the metric-affine gauge theory of gravity (MAG), generalized the Poincaré gauge theory of gravity with non-vanishing nonmetricity tensor [9,10]. Later on, the papers [11][12][13][14][15] suggested that the renormalizability and unitarity problems in quantum gravity can be solved by taking the affine group as the dynamical group in a gauge theory of gravity by the help of general linear connection Γ α µν [10]. There is an interesting study which is based on GL(4, R) gauge theory of gravity, proposes a unified theory between the electromagnetic and gravitation fields in the concept of purely affine formulation of the Einstein-Maxwell theory [16].…”