Regimes — Quantum Field Theory

TriadicFrameworks /docs/theories/quantum_field_theory/regimes.md#

Quantum Field Theory (QFT) behaves differently across regimes R1 → R4.
These regimes describe how fields, excitations, symmetries, and
renormalization behave as energy, coherence, and scale change.

QFT is a substrate‑level excitation grammar, so its regime boundaries
are defined by:

• amplitude structure
• excitation stability
• symmetry geometry
• renormalization flow
• substrate resonance

R1 — Quantum Amplitude Regime#

(No stable excitations • field reduces to amplitude structure)#

In R1:

• fields collapse to quantum amplitudes
• no stable excitations exist
• creation/annihilation operators lose physical meaning
• propagators reduce to amplitude kernels
• symmetry generators act trivially
• vacuum structure is undefined

QFT reduces to Quantum Mechanics in this regime.

Interpretation:
QFT cannot produce stable modes in R1.

R2 — Canonical QFT#

(Stable excitations • renormalization active • Lorentz geometry intact)#

In R2:

• stable excitation modes exist
• creation/annihilation operators are well‑defined
• propagators encode correlation structure
• gauge geometry is stable
• renormalization flow is finite
• vacuum structure is well‑defined
• symmetry generators produce conserved quantities

This is the regime where:

• the Standard Model lives
• most of physics operates
• QFT is fully coherent

Interpretation:
R2 is the canonical QFT regime.

R3 — High‑Energy Resonance Regime#

(Symmetry restoration • resonance surfaces merge • couplings run)#

In R3:

• renormalization flow dominates
• couplings run toward unification
• symmetry groups partially restore
• excitation surfaces merge
• vacuum structure flattens
• high‑energy resonance topology emerges

This is the regime of:

• electroweak symmetry restoration
• asymptotic freedom
• early‑universe field behavior

Interpretation:
QFT becomes a resonance‑topology theory in R3.

R4 — Cosmological Regime#

(QFT incomplete • horizon‑scale fields dominate)#

In R4:

• QFT breaks down
• horizon‑scale fields dominate
• vacuum structure becomes cosmological
• renormalization loses meaning
• field theory requires cosmology or quantum gravity

This is the regime of:

• inflation
• dark energy
• horizon‑scale coherence
• cosmic background fields

Interpretation:
QFT cannot describe R4 without cosmology.

Summary#

Quantum Field Theory behaves as:

• R1: amplitude‑only
• R2: stable excitation grammar
• R3: high‑energy resonance topology
• R4: cosmological breakdown

QFT is coherent in R2 → R3, collapses in R1, and is incomplete in R4.