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