Wave Equations on a de Sitter Fiber Bundle

Abstract

AbstractA gauge theory of strong interaction is developed based on fields defined on a fiber bundle. The structural group of the bundle is taken to be the L4,1 de Sitter group. An internal variable ε, varying in the fiber over a space‐time point x, is introduced as a means to describe – with the help of a semiclassical wave function PS(x, ε) defined on the bundle space – the internal structure of extended hadrons in a framework using differential geometric techniques. Three basic nonlinear wave equations for PS(x, ε) are established which are of integro‐differential type. The nonlinear coupling terms in these de Sitter gauge invariant equations represent physically a generalized spin orbit coupling or a generalized spin spin coupling for the motion taking place in the fiber. The motivation for using a bigger space for the definition of hadronic matter wave functions as well as the implications of this geometric approach to strong interaction physics is discussed in detail, in particular with respect to the problem of hadronic constituents. The proposed fiber bundle formalism allows a dynamical description of extended structures for hadrons without implying the necessity of introducing any constituents.