# Coherence Map — Quantum Field Theory  
### TriadicFrameworks /docs/theories/quantum_field_theory/coherence_map.md

Quantum Field Theory (QFT) maintains coherence when its substrate-level  
structures — fields, operators, symmetries, renormalization, and vacuum  
geometry — remain internally consistent. This map defines how coherence  
is measured, maintained, and lost across regimes R1 → R4.

QFT coherence is not about particles or forces.  
It is about **operator algebra**, **symmetry geometry**, **excitation  
stability**, and **renormalization flow**.

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# 1. Coherence Dimensions

QFT coherence is evaluated across six substrate dimensions:

### **1. Field‑Structure Coherence**  
- Fields must maintain well‑defined transformation rules.  
- Lorentz invariance must hold.  
- Field content must remain stable under renormalization.

### **2. Operator‑Algebra Coherence**  
- Commutation/anticommutation relations must remain valid.  
- Creation/annihilation operators must remain well‑defined.  
- Path integrals must remain finite and consistent.

### **3. Symmetry‑Geometry Coherence**  
- Gauge symmetries must remain unbroken (unless broken by vacuum).  
- No anomalies in conserved currents.  
- Group generators must remain consistent across scales.

### **4. Vacuum‑Structure Coherence**  
- Vacuum expectation values must remain stable.  
- Vacuum energy must remain finite (renormalized).  
- Stability surfaces must not collapse.

### **5. Renormalization‑Flow Coherence**  
- β‑functions must remain finite.  
- Couplings must run smoothly with energy.  
- No divergence or loss of predictivity.

### **6. Excitation‑Stability Coherence**  
- Excitations must remain stable modes of fields.  
- Propagators must remain well‑defined.  
- Mass and resonance profiles must remain finite.

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# 2. Coherence Across Regimes

## **R1 — Amplitude Collapse (Low‑Coherence)**  
- Field structure collapses to amplitude structure.  
- No stable excitations.  
- Operator algebra reduces to QM.  
- Vacuum undefined.  
- Symmetry trivial.

**Coherence Level:** C1 (minimal)

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## **R2 — Canonical QFT (High‑Coherence)**  
- Stable excitations.  
- Operator algebra fully valid.  
- Gauge geometry intact.  
- Renormalization finite.  
- Vacuum stable.

**Coherence Level:** C4 (maximal)

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## **R3 — High‑Energy Resonance (Medium‑High Coherence)**  
- Symmetry restoration begins.  
- Couplings run toward unification.  
- Vacuum flattens.  
- Excitation surfaces merge.  
- Renormalization dominates.

**Coherence Level:** C3 (stable but shifting)

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## **R4 — Cosmological Regime (Low‑Medium Coherence)**  
- QFT incomplete.  
- Horizon‑scale fields dominate.  
- Vacuum becomes cosmological.  
- Renormalization loses meaning.  
- Requires cosmology module.

**Coherence Level:** C2 (partial)

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# 3. Coherence Failure Modes

QFT coherence fails when:

- Lorentz invariance breaks  
- renormalization diverges  
- anomalies appear in symmetry currents  
- vacuum becomes unstable  
- operator algebra becomes inconsistent  
- excitations lose stability  

These failures indicate a transition out of R2 → R3.

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# 4. Coherence Gradient Field

QFT’s coherence gradient measures sensitivity to:

- field‑structure drift  
- operator‑algebra instability  
- symmetry‑geometry deformation  
- vacuum‑surface curvature  
- renormalization divergence  
- excitation‑surface collapse  

High gradients indicate **approaching regime boundaries**.

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# 5. Summary

Quantum Field Theory is coherent when:

- fields transform correctly  
- operators obey algebraic rules  
- symmetries remain geometric  
- vacuum remains stable  
- renormalization remains finite  
- excitations remain stable modes  

QFT is maximally coherent in **R2**, partially coherent in **R3**,  
collapses in **R1**, and becomes incomplete in **R4**.