Connect refined state construction to Fock-space dynamics

Establish a precise mathematical relation between the refined quantum state ω^t_V defined via group-averaged surface layer integrals and the unitary time evolution on bosonic/fermionic Fock spaces developed in this paper for causal fermion systems.

Background

Previous work defined a refined state by averaging over unitary transformations of the measure using surface layer integrals. The present paper derives a unitary Fock-space dynamics leading to QED in a limiting case.

How these two structures correspond—i.e., how the refined state encodes or reproduces the unitary evolution—remains technically unresolved.

References

On a technical level, at present it is unclear how to relate the refined state (equation (statedef)) to the constructions in the present paper.

— Holographic Mixing and Fock Space Dynamics of Causal Fermion Systems  (2410.18045 - Dappiaggi et al., 2024) in Section 7 (The Dynamics of the Quantum State)