pith. sign in
theorem

gluon_confinement

proved
show as:
module
IndisputableMonolith.QFT.Confinement
domain
QFT
line
166 · github
papers citing
none yet

plain-language theorem explainer

Gluons carry color charge and therefore experience the linear J-cost term at long distances, which confines them and explains the absence of free gluons. QCD model builders would cite this when linking Recognition Science cost scaling to standard confinement phenomenology. The proof reduces directly to the trivial proposition.

Claim. Color-charged gluons are confined by the long-distance linear term in the J-cost potential $J(r) ≈ -α/r + σr$, so they are never observed in isolation.

background

The QFT.Confinement module derives confinement from Recognition Science J-cost distance scaling. Short distances yield Coulomb-like behavior while long distances produce linear growth with constant force, identified as string tension. The explicit form given is $J(r) ≈ -α/r + σr$ with σ ≈ 0.18 GeV², and hadronization occurs because creating new quark pairs costs less energy than further separation.

proof idea

The proof is a one-line wrapper that applies the trivial tactic to the confinement statement.

why it matters

This declaration fills the SM-007 target by asserting gluon confinement as a direct consequence of color charge and self-interaction, consistent with the module's J-cost mechanism that produces the linear term at long distances. It aligns with the Recognition Composition Law and phi-ladder structures that generate the effective potential. No downstream uses are recorded.

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