Field theories in terms of particle-string variables: Spin, internal symmetries, and arbitrary dimension

We provide essential tools for a program of rewriting field theories in terms of particle-string variables. The general methods are illustrated in the case of quantum chromodynamics: (1) We find the particle-trajectory representation for the quark Green's functional. (2) Thus, we derive directly correct end-point terms for quarks at the ends of strings. (1) and (2) are for any number of dimensions. (3) In two dimensions, we find a functional bridge from quantum chromodynamics to the Bardeen-Bars-Hanson-Peccei string