Analytic Derivation of the String Tension From Nonlinear Elastic Media to Quark Confinement

Lattice QCD numerically gives the string tension σ ≈ 0.9 GeV/fm, but cannot derive this value analytically from first principles. This paper provides a rigorous analytical formula for the string tension within the Gluon Elastic Lattice Theory (GELT): σ = ζσ η K_0 d_0^2, where ζσ is a dimensionless constant emerging from the cross-sectional integral of the tube geometry, η is the strain hardening coefficient of the medium, K_0 is the background stiffness, and d_0 is the lattice spacing. Substituting the precisely determined GELT parameters yields σ ∼ 1 GeV/fm in order of magnitude. The string tension — the slope of the linear confining potential — is an inevitable consequence of the hardening response of a nonlinear elastic medium to stretching. Quark confinement is not a QCD postulate to be accepted, but a directly computable mechanical quantity determined by basic medium parameters.