Do electrons tunnel from the vacuum the same way in two formulations of quantum field theory?

When a powerful electric field tears electron-positron pairs from the quantum vacuum—a phenomenon called Sauter-Schwinger pair creation—the probability depends on how you set up the calculation. Using Feynman's spacetime picture, researchers solved the governing equation (Dirac equation) two different ways: one treating it as a boundary-value problem, another as an initial-condition problem. Both gave nearly identical total pair production rates but produced starkly different predictions for the spin orientations of the created particles, suggesting the choice of mathematical approach matters more than expected.