Essential Nonlocality of Spin- and Polarization-Resolved Distributions in Strong-Field Quantum Electrodynamics

Spin and polarization are central to precision tests of fundamental physics and for interpreting emission from astrophysical sources and ultraintense laser-matter experiments. Predictive modeling therefore requires not only energy spectra, but also angle-, spin-, and polarization-resolved particle distributions. As a paradigmatic example, we focus on nonlinear Compton scattering, i.e., the emission of radiation by a charge in a strong electromagnetic field. In the locally constant field approximation (LCFA), this process is modeled by Monte-Carlo sampling of time-local differential LCFA rates evaluated from the instantaneous particle state. Here we show that, once photon emission angles and electron/photon spin and polarization are resolved, the resulting time-local fully differential LCFA expression can become negative even in a uniform constant crossed field. This leads to unphysical predictions, such as spin and Stokes vectors with magnitude exceeding unity. We demonstrate that a consistent probabilistic description is recovered only after integrating over the full photon formation region, and we derive closed analytical expressions for the resulting formation-region-integrated spin- and polarization-resolved distributions. Based on these results, we introduce a model that assigns spin and polarization from formation-region-integrated amplitudes evaluated in an event-by-event matched auxiliary constant crossed field determined by local invariants. Simulations of a laser-electron-beam collision and of emission in a pulsar-like magnetic field reveal spin and polarization patterns that differ qualitatively from current instantaneous-particle-state emission models. These findings have direct implications for strong-field QED experiments and for interpreting polarized radiation from astrophysical sources.