APPLICATION OF THE GROUP OF PATHS TO THE GAUGE-THEORY AND QUARKS

A description is presented of a charged particle in an external gauge field with the help of a previously introduced group of paths. This description exploits the group representation induced by known contour factors (ordered exponents, holonomy group). Then some novel class of representations is defined by integration of covariantly constant 2-forms. The representation from this class connected with the dual form * F for the strength of field F is shown to describe analogues of test magnetic monopoles and dyons in the gauge theory. The quarks are supposed to be gauge dyons, whose 'magnetic' degrees of freedom are connected with a colour. © 1979 D. Reidel Publishing Company.