Quarks at the ends of the string

Abstract

We develop a technique for attaching quark quantum numbers to world lines joined by relativistic strings. We are able to describe spin-0 and spin-½ $\mathrm{U}\mathrm{}\left(n\right)\mathrm{}$-symmetric quarks attached to world lines. One spin-½ theory based on the Dirac equation yields a classical particle with helical motion, interpretable as Zitterbewegung. Another spin-½ model has no helical motion, but yields an algebra resembling that of super-symmetry. Motivated by duality diagrams and some general properties of quarkgluon models, we then construct quark-string models of mesons and baryons. The analysis of the meson model with unequal quark masses implies a stringlike spectrum with broken trajectory intercepts. A simple baryon model suggests a dynamical reason for diquark configurations in the lowest states. Physical weak and electromagnetic currents for the quark-string system follow from a minimal-coupling scheme as in gauge field theories.