Editing Openai/6897769e-4ee4-800f-aba5-69cca34f701c (section)

=== 1. Adding spins is not sufficient. We did not literally add spin-1 + spin-1 = spin-2. Instead, we constructed a symmetric rank-2 composite operator from two vector fields and showed how its two-point correlator can exhibit the right projector and pole structure to mimic a spin-2 massless propagation. That is the QFT-legitimate route. ===
# Loop suppression & coherence. Fermion loops and two-photon processes are usually suppressed (powers of eee and factors of 1/m1/m1/m). Getting a large effective GeffG_{\rm eff}Geff requires strong coherence (many photons/photon modes adding in phase) or another amplification mechanism (boundary density of states, geometric factors like 4πR24\pi R^24πR2 producing large NNN scaling).
# Known analogues: physics offers precedents where composite fields emerge: - Nambu–Jona-Lasinio: composite scalars from fermion bilinears. - Double copy / BCJ relations: classical gravity solutions building from gauge fields. - Casimir and van der Waals: multi-photon exchange between neutral bodies yields effective long-range interactions (though with different power laws unless coherence is enforced). Use these as sanity checks: the formal steps are analogous, but the physical scaling and signs must be checked case by case.
# Gauge and renormalization subtleties. Composite operators require renormalization mixing; the projector isolation of the spin-2 part must be done carefully (project onto TT sector, remove trace parts).