proposition 108.59 The hypercharge coupling and its pole

Rests on

• depends_on corollary 108.20 What is physical in a beta function ¶
  • depends_on equation 108.24 eq:rg-beta-series ¶
  • depends_on theorem 102.35 Asymptotic freedom ¶
    • depends_on equation 14.80 eq:lie-su3-roots ¶
    • depends_on equation 102.31 eq:qcd-casimirs ¶
    • depends_on theorem 102.33 The one-loop coefficient, from a magnetic response ¶
      • depends_on equation 102.19 eq:qcd-alpha-s-def ¶
      • depends_on lemma 102.31 The vacuum's two responses are reciprocal ¶
        • depends_on equation 102.19 eq:qcd-alpha-s-def ¶ ↺
        • depends_on postulate 38.2 Invariance of the speed of light ¶
        • proves proof ch:04-qcd@proof-14 ¶
      • depends_on lemma 102.32 Landau levels with $g=2$ ¶
        • depends_on equation 93.2 eq:dirac-g2 ¶
        • depends_on equation 102.28 eq:qcd-ym-expanded ¶
        • proves proof ch:04-qcd@proof-15 ¶
      • proves proof ch:04-qcd@proof-16 ¶
    • proves proof ch:04-qcd@proof-18 ¶
  • depends_on theorem 108.19 The first two beta coefficients are scheme independent ¶
    • depends_on proposition 100.55 Scheme independence of observables ¶
      • depends_on definition 100.46 On-shell renormalization conditions ¶
      • depends_on definition 100.54 Two schemes ¶
      • proves proof ch:02-qed-renormalization@proof-30 ¶
    • proves proof ch:10-renormalization-group@proof-8 ¶
  • proves proof ch:10-renormalization-group@proof-9 ¶
• depends_on equation 104.13 eq:ewh-gell-mann-nishijima ¶
• depends_on equation 102.35 eq:qcd-beta-master ¶
• proves proof ch:10-renormalization-group@proof-26 ¶

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