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.