Extension of worldline computational algorithms for QCD to open fermionic contours

TL;DR

This paper extends worldline computational algorithms in QCD to include open fermionic paths, enabling efficient calculations of fermionic propagators and processes involving external fermionic states within a geometric framework.

Contribution

It introduces new algorithms for open fermionic paths in the worldline formalism, broadening the applicability of QCD computations to fermionic propagators and external states.

Findings

Algorithms for fermionic propagators are established.

The framework emphasizes Wilson line operators as the core of dynamics.

Geometrical properties like Polyakov's spin factor are integral to the formalism.

Abstract

The worldline casting of a gauge field system with spin-1/2 matter fields has provided a, particle-based, first quantization formalism in the framework of which the Bern-Kosower algorithms for efficient computations in QCD acquire a simple interpretation. This paper extends the scope of applicability of the worldline scheme so as to include open fermionic paths. Specific algorithms are established which address themselves to the fermionic propagator and which are directly applicable to any other process involving external fermionic states. It is also demonstrated that in this framework the sole agent of dynamics operating in the system is the Wilson line (loop) operator, which makes a natural entrance in the worldline action; everything else is associated with geometrical properties of particle propagation, of which the most important component is Polyakov's spin factor.