Currents in a theory of strong interaction based on a fiber bundle geometry

A fiber bundle constructed over spacetime is used as the basic underlying framework for a differential geometric description of extended hadrons. The bundle has a Cartan connection and possesses the de Sitter group SO(4,1) as structural group, operating as a group of motion in a locally defined space of constant curvature (the fiber) characterized by a radius of curvature Rapprox. =10-13 cm related to the strong interactions. A hadronic matter field psi (x,xi) is defined on the bundle space, with x the spacetime coordinate and xi varying in the local fiber. The components of a generalized tensor current zeta/sup( m)//sub muab/(x) are introduced, involving a bilinear expression in the fields psi (x,xi) and psi (x,xi) integrated over the local fiber at the point x. This hadronic matter current is considered as a source current for the underlying fiber geometry by coupling it in a gauge-invariant manner to the curvature expressions derived from the bundle connection coefficients, which are associated here with strong interaction effects, i.e., play the role of meson fields induced in the geometry. Studying discrete symmetry transformations between the 16 differently soldered Cartan bundles, a generalized matter-antimatter conjugation C is established which leaves the basic current-curvature equations C-invariant. The discrete symmetry transformation C turns out to be the direct product of an ordinary charge conjugation for the Dirac point-spinor part of psi (x,xi) and an internal PT transformation applied globally on the bundle to the fiber (i.e., de Sitter) part of psi