# Cross‑Module Integration — Quantum Field Theory  
### TriadicFrameworks /docs/theories/quantum_field_theory/cross_module.md

Quantum Field Theory (QFT) is the **substrate‑level excitation grammar**  
that underlies all modern physics. Every module that uses excitations,  
symmetry geometry, or resonance behavior inherits structure from QFT.

This file describes how QFT integrates with other TriadicFrameworks  
modules across the RTT stack.

---

# 1. Integration with Quantum Mechanics (QM)

**Inheritance:**  
- amplitude structure  
- operator algebra  
- Hilbert space foundations  

**Exports to QFT:**  
- commutation/anticommutation rules  
- probabilistic amplitude interpretation  

**QFT adds:**  
- Lorentz invariance  
- field operators  
- creation/annihilation structure  

**Regime link:**  
- R1: QFT collapses to QM  
- R2: QFT extends QM to fields  

---

# 2. Integration with Special Relativity (SR)

**Inheritance:**  
- Lorentz geometry  
- spinor/tensor representations  
- relativistic invariance  

**Exports to QFT:**  
- transformation rules for fields  
- constraints on operator algebra  

**QFT adds:**  
- relativistic excitation modes  
- covariant propagators  

**Regime link:**  
- R2: SR fully active  
- R3: symmetry restoration modifies SR behavior  

---

# 3. Integration with the Standard Model (SM)

**QFT provides:**  
- fields  
- operators  
- propagators  
- symmetry generators  
- renormalization structure  

**SM adds:**  
- sector grammar  
- gauge geometry  
- Higgs stabilization  
- flavor structure  

**Regime link:**  
- R2: SM stable  
- R3: SM symmetry restoration emerges from QFT  

---

# 4. Integration with Thermodynamics

**QFT provides:**  
- high‑energy resonance behavior  
- running couplings  
- vacuum structure  

**Thermodynamics adds:**  
- entropy flow  
- equilibrium behavior  
- statistical ensembles  

**Regime link:**  
- R3: thermodynamic behavior emerges from QFT resonance  
- R4: thermodynamics dominates over QFT  

---

# 5. Integration with Cosmology

**QFT provides:**  
- early‑universe field behavior  
- vacuum energy structure  
- symmetry restoration  

**Cosmology adds:**  
- horizon‑scale fields  
- inflationary dynamics  
- cosmic background structure  

**Regime link:**  
- R3 → R4: QFT becomes incomplete  
- R4: cosmology required  

---

# 6. Integration with Information Theory

**QFT provides:**  
- state classification  
- symmetry labels  
- operator algebra  

**Information Theory adds:**  
- encoding/decoding structure  
- entropy measures  
- channel capacity  

**Regime link:**  
- R2: QFT states fully classifiable  
- R3: classification shifts under symmetry restoration  

---

# 7. Integration with Framework Field Theory (FFT)

**QFT provides:**  
- substrate‑level field grammar  
- operator algebra  
- resonance surfaces  

**FFT adds:**  
- meta‑field structure  
- cross‑module propagation  
- coherence‑layer mapping  

**Regime link:**  
- FFT spans R1 → R4  
- QFT occupies R2 → R3  

---

# 8. Integration Summary

QFT is the substrate ancestor of:

- Standard Model  
- Gauge Theories  
- Thermodynamics  
- Cosmology  
- Information Theory  
- Framework Field Theory  

QFT inherits from:

- Quantum Mechanics  
- Special Relativity  

QFT exports:

- fields  
- operators  
- propagators  
- symmetry geometry  
- renormalization flow  
- vacuum structure  

QFT is the **substrate grammar** that binds the entire canon.