The gauge principle and non-abelian Lie algebras

Does integrating the one-loop QCD beta function down and up from αₛ(M_Z) = 0.118 reproduce the couplings measured at the tau mass and at 1 TeV, and where does it fail? Useful evidence includes c_F = 4/3 at the quark-gluon vertex and C_A = 3 inside β₀ = 11 - 2n_f/3, both from Gell-Mann trace identities in NumPy; αₛ(Q) from a SciPy integration matched across the m_c, m_b and mₜ flavour thresholds and overlaid on measured points; and the Landau pole at Q = Λ_QCD marking where one loop dies..

This GioPhysics course map is an adaptable learning sequence, not academic credit, accreditation, or a universal university syllabus. It is written for a four-credit course of roughly three lecture hours plus two to three laboratory or computational hours a week across fifteen weeks, and it is deliberately more mathematical than University Physics I–IV: linear algebra and differential equations are working tools here, not background. Twenty units are mapped against a suggested fifteen-week delivery, so several units share a teaching week. Departments differ widely in how much formalism they expect at this stage; follow your institution's published scope, notation, laboratory programme, and assessment rules. A result should be checked against units, signs, limiting cases, and the conditions under which its model was derived.