Unified affine gauge theory of gravity and strong interactions with finite and infinite [formula omitted] spinor fields

Abstract

A theory in which the Linear Group in four dimensions GL(4, R) and its Affine Extension GA(4, R) bear a direct relationship to the Physics of hadrons, and indirectly to that of the leptons is outlined. The Poincare group is embedded in a Global GA(4, R) Symmetry. Hadrons correspond to (infinite-dimensional) unitary representations of GA(4, R) , as defined by their GL(3, R) or SL(3, R) bandor content. These SL(3, R) bandors are embedded in infinite-component (poly-) fields, representing SL(4, R) bandors. All multiplicity free unitary irreducible representations are explicitly constructed, and the formulas for the scalar products of the representations' Hilbert spaces as well as the matrix elements for all noncompact (shear) operators are given. Leptons are described by nonlinear representations of GL(4, R) , realized through a Metric tensor field (i.e. Gravity). Nonlinear representations of GL(4, R) are presented in detail. The anholonomic description in terms of tetrad deformations is used. GA(4, R) is then postulated as a local Gauge Theory. It generates an Einstein-like Gravitational Interaction, plus a Confining Strong Interaction which applies only to the linear representations, i.e. to hadrons. Local GA(4, R) symmetry is spontaneously broken to local Poincare invariance for leptons (Einstein-Cartan Gravity). The variations of all the fields in the theory are presented and the Noether currents are derived. The choice of a Lagrangian that could explain hadron confinement is discussed.