Extend Dirac particle path-integral representation to more general external fields

Determine how to extend the path integral representation for Dirac particles in electromagnetic fields (as proposed by Angelantonj et al. and related works) to more general external field configurations while preserving mathematical and physical consistency of the formulation.

Background

The paper reviews prior attempts to construct path-integral formulations connected to the Dirac equation. It notes that specific representations tailored for Dirac particles in electromagnetic fields have been proposed, but their generalization remains problematic. The authors explicitly state that extending these methods to broader classes of external fields while maintaining consistency is unresolved.

This open issue is presented in the context of the broader challenge of unifying non-relativistic and QED-based path-integral formulations and constructing a spinor-form path integral that bridges classical and quantum relativistic mechanics.