What question did this study set out to answer?

The research aims to demonstrate two key properties of Quantum Chromodynamics (QCD) as geometric theorems derived from foam topology.

March 19, 20262 citationsOpen Access

Asymptotic Freedom and Quark Confinement as Geometric Theorems from Foam Torsion Topology

View Full Paper

LMLuke Martin

Key Points

The research aims to demonstrate two key properties of Quantum Chromodynamics (QCD) as geometric theorems derived from foam topology.
Proved asymptotic freedom and quark confinement as theorems using geometric inequalities.
Analyzed the dimensional properties of T₂g within the context of quark behavior.
Examined fractional torsion winding numbers to establish confinement.
Asymptotic freedom is shown to result from a geometric inequality involving dimensionality and the number of flavors.
Quark confinement identified as a consequence of topological invariants related to torsion.
String tension determined as a constant derived from the geometric properties of the model.

Abstract

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: b₀QCD=7>0 because dim (T₂g) ×11 > 2×nf (33>4, CA=3, nf=6) — a geometric inequality, not a perturbative result. Exact identity: b₀QCD=7=λT₂g=CA²−2. 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.

AIに質問

Bookmark

View Full Paper

Cite This Study

Luke Martin (Tue,) studied this question.

synapsesocial.com/papers/69bb9313496e729e62980efc https://doi.org/https://doi.org/10.5281/zenodo.19064581

AIに質問

Bookmark

View Full Paper