No well-defined probability measure exists for the classical Kolmogorov path integral representation of the Dirac equation in Minkowski space, as the propagator's distributional character and the metric's indefinite signature are two sides of one measure-theoretic obstruction.
Path Integrals for the Telegrapher’s and Dirac Equations; the Analytic Family of Measures and the Underlying Poisson Process,
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Quantum Simulation of Hyperbolic Equations and the Nonexistence of a Dirac Path Measure
No well-defined probability measure exists for the classical Kolmogorov path integral representation of the Dirac equation in Minkowski space, as the propagator's distributional character and the metric's indefinite signature are two sides of one measure-theoretic obstruction.