Asymptotic Freedom and Quark Confinement as Geometric Theorems from Foam Torsion Topology
Asymptotic Freedom and Quark Confinement as Geometric Theorems from Foam Torsion Topology
Two defining properties of QCD — asymptotic freedom and quark confinement — are proved as theorems from the foam geometry, requiring no dynamical calculation. Asymptotic Freedom Theorem: b₀^QCD=7>0 because dim(T₂g)×11 > 2×n_f (33>4, C_A=3, n_f=6) — a geometric inequality, not a perturbative result. Exact identity: b₀^QCD=7=λ_T₂g=C_A²−2. Confinement Theorem: fractional T₂g torsion winding numbers (quarks: ±1/3, ±2/3) cannot propagate as free asymptotic states because π₁(T₂g vacuum)=ℤ makes integer winding number a topological invariant. String tension σ=3k/2. Both results follow from torsion topology independently of coupling strength.
beta function, Casimir operators, UFFT, torsion topology, asymptotic freedom, string tension, quark confinement, foam geometry, winding number, QCD
beta function, Casimir operators, UFFT, torsion topology, asymptotic freedom, string tension, quark confinement, foam geometry, winding number, QCD
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