Nonperturbative Glueball Spectrum and Confinement from Temporal Memory in QCD

This work presents Paper XXXII of the History-Dependent Gravity (HDG) series, demonstrating that color confinement and the glueball spectrum in QCD can be derived analytically from a temporal memory kernel in the effective action. Key Results: Analytic Confinement: We prove that an infrared spectral density of temporal memory modes ρ(μ2)∼1/μ2ρ(μ2)∼1/μ2 dynamically drives the dressed gluon propagator to a unique scaling solution, DG(p2)∼1/p4DG(p2)∼1/p4. A rigorously regulated Fourier transform of this propagator yields a linear static potential V(r)=σrV(r)=σr, establishing the Wilson loop area law without ad hoc assumptions. Glueball Spectrum: Employing the same spectrally-resolved interaction kernel, we construct and solve the homogeneous Bethe-Salpeter equation (BSE) for two-gluon bound states. After symmetric discretization and partial-wave projection, the numerical solution yields a bare scalar glueball mass M0++=2.038M0++=2.038 GeV. Bound-State Structure: The extracted Bethe-Salpeter amplitude is smooth, node-free, and strongly peaked in the infrared (p∼ΛHDGp∼ΛHDG), yielding a mean-square radius rrms≈0.53rrms≈0.53 fm. This confirms a compact, infrared-dominated gluonic configuration, consistent with independent QCD sum rule and DSE estimates for the unmixed gluonic component. These results establish temporal nonlocality as a unifying microscopic mechanism linking the infrared structure of the gluon propagator, color confinement, and hadron formation.