Extension of worldline computational algorithms for QCD to open fermionic contours

The worldline casting of a gauge field system with spin-1/2 matter fields h as provided a, particle-based, first quantization formalism in the framewor k of which the Bern-Kosower algorithms for efficient computations in QCD ac quire a simple interpretation. This paper extends the scope of applicabilit y of the worldline scheme so as to include open fermionic paths. Specific a lgorithms are established which address themselves to the fermionic propaga tor and which are directly applicable to any other process involving extern al fermionic states. It is also demonstrated that in this framework the sol e agent of dynamics operating in the system is the Wilson line (loop) opera tor, which makes a natural entrance in the worldline action; everything els e is associated with geometrical properties of particle propagation, of whi ch the most important component is Polyakov's spin factor.