Classical Dynamics of Rotating Relativistic String with Massive Ends: the Regge Trajectories and Quark Masses

摘要

Dynamic equations in the theory of a relativistic string with point masses at the ends are formulated in terms of geometric invariants of the world trajectories of the massive ends of the string (curvature k(sub i) and torsion (kappa)(sub i)((tau)), i=1,2 of the trajectories). With these characteristics we reproduce the string world surface up to its position in Minkowski space E(sub 2)(sup 1). The torsions (kappa)(sub i)((tau)), i=1,2 obey a system of second order differential equations with delay arguments describing the retardation effects of the interaction of masses through the string, k(sub i) being constants. The constant torsions are investigated in detail. In this case the string world sheet is a helicoid in E(sub 2)(sup 1). A nonlinear relation (the Regge trajectory) between the angular momentum of the system, J and the mass squared, M(sup 2), is derived. For given meson masses (M) and spin (J), the masses of quarks are calculated. 14 refs., 1 fig., 1 tab. (Atomindex citation 26:045765)