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Physical validity of the scale separation ℓ_Λ ≫ ℓ_min

Determine whether the scale-separation condition that the dephasing length scale ℓ_Λ is much larger than the nonlocality scale ℓ_min is satisfied in physically realistic causal fermion systems.

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Background

Several constructions, including a perturbative/microlocal expansion for the unitary holographic mixing operator, rely on the assumption that the phase-oscillation scale is much larger than the nonlocality scale.

The authors emphasize that it is presently unclear whether this assumption holds in realistic physical settings, leaving a key modeling question unresolved.

References

However, there remains the limitation that the length scale ℓΛ on which the phase factors oscillate (see (Lamscale)) must be much larger than ℓ{\min}. At present, it is not clear whether this condition is satisfied in physically realistic situations.

— Holographic Mixing and Fock Space Dynamics of Causal Fermion Systems (2410.18045 - Dappiaggi et al., 23 Oct 2024) in Section 5.1 (Preparatory Considerations)