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.
A sampling method for determining th e lowest eigen- values and the principal eigenfunction of the Schr¨ odinger’s equat ion,
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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.