Origin and scope of the spontaneous cancellation mechanism in equal-time correlators

Characterize and explain the spontaneous cancellation mechanism that renders equal-time correlators of conserved densities independent of cutoff parameters in the studied examples, determine its mathematical and physical origin, and ascertain why this mechanism appears to be specific to equal-time correlators.

Background

Throughout several examples, the authors find that while equal-time correlators of frame-dependent variables (e.g., velocity) depend on cutoff scales, the equal-time correlators of conserved densities match standard nonrelativistic results and become independent of the cutoff when the stochastic and deterministic cutoff scales coincide.

They attribute this to a spontaneous cancellation mechanism but expressly state that they do not yet understand it. Clarifying this mechanism would improve understanding of the robustness of predictions and delineate when such cancellations occur.