Relate stationary-phase dephasing to group-integral dephasing

Determine whether and how the stationary-phase dephasing analysis in position space developed in this paper is mathematically related to the unitary group integral saddle-point method used in prior work for dephasing and entanglement in causal fermion systems, and characterize any equivalence or correspondence between the two approaches.

Background

The paper derives quantum electrodynamics from causal fermion systems by modeling dephasing via stationary phase methods in position space. Earlier work achieved dephasing using unitary group integrals with saddle-point analysis to construct quantum states and entanglement.

The authors explicitly note that these two techniques seem complementary yet their precise relationship is unknown, motivating a direct mathematical comparison of the approaches.