Effects of a space–time dependent topological noise term

Determine the modifications to the stochastic equations of motion induced by a space–time dependent topological noise operator quadratic in the advanced field, specifically when the coefficient θ2 depends on space and time, and assess the physical implications of these contributions in open electromagnetism.

Background

The paper introduces a novel topological noise operator quadratic in the advanced field that is a total derivative when its coefficient θ2 is constant. The authors note that if θ2 varies in space and time, integrations by parts generate new contributions to the stochastic sector.

They leave the analysis of these induced terms—how they enter the stochastic equations and affect dynamics—as an open direction.