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Part XI ›
The Renormalization Group
The Renormalization Group
foundations results +18 more equations +13 more phenomena owed depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) notation 108.1: The renormalization scale, and what it is 108.1 The renormalizat… notation 108.2: Reduced fields and the dimension of an operator 108.2 Reduced fields a… definition 108.6: The effective coupling 108.6 The effective co… definition 108.10: Bare and renormalized Green functions 108.10 Bare and renorma… definition 108.12: Beta function and anomalous dimensions 108.12 Beta function an… definition 108.17: Four schemes 108.17 Four schemes notation 108.30: Units in the statistical sections 108.30 Units in the sta… definition 108.31: The block transformation 108.31 The block transf… definition 108.34: The Wilsonian transformation 108.34 The Wilsonian tr… definition 108.42: Fixed point and linearized flow 108.42 Fixed point and… definition 108.78: Dilatations and the trace of the stress tensor 108.78 Dilatations and… proposition 108.3: The SI dimension of a coupling 108.3 The SI dimension… theorem 108.7: The Gell-Mann–Low functional equation 108.7 The Gell-Mann–Lo… corollary 108.8: The flow is integrable in closed form 108.8 The flow is inte… theorem 108.11: The Callan–Symanzik equation 108.11 The Callan–Syman… proposition 108.13: Solution by characteristics 108.13 Solution by char… corollary 108.14: Anomalous scaling at a fixed point 108.14 Anomalous scalin… theorem 108.18: 't~Hooft's mass-independence 108.18 't~Hooft's mass-… theorem 108.19: The first two beta coefficients are scheme
independent 108.19 The first two be… corollary 108.20: What is physical in a beta function 108.20 What is physical… proposition 108.22: A coupling's dimension away from four 108.22 A coupling's dim… corollary 108.23: Where \barμ comes from, and why it must be
arbitrary 108.23 Where \barμ come… theorem 108.26: Power counting in 3+1 108.26 Power counting i… corollary 108.27: The three classes 108.27 The three classes equation 108.2: eq:rg-reduced-scalar eq. (108.2) equation 108.3: eq:rg-operator-dimension eq. (108.3) equation 108.4: eq:rg-coupling-dimension eq. (108.4) equation 108.5: eq:rg-hatted-coupling eq. (108.5) equation 108.6: eq:rg-effective-strength eq. (108.6) equation 108.9: eq:rg-flow-equation eq. (108.9) equation 108.12: eq:rg-green-def eq. (108.12) equation 108.14: eq:rg-beta-gamma-def eq. (108.14) equation 108.16: eq:rg-characteristic-solution eq. (108.16) equation 108.24: eq:rg-beta-series eq. (108.24) equation 108.27: eq:rg-lambda-dimension-d eq. (108.27) equation 108.29: eq:rg-superficial-degree eq. (108.29) equation 108.34: eq:rg-exponents-from-eigenvalues eq. (108.34) phenomenon 108.49: A critical exponent, and a disagreement 108.49 A critical expon… phenomenon 108.56: The strong coupling runs as
predicted 108.56 The strong coupl… phenomenon 108.73: Neutrino mass points above the electroweak scale 108.73 Neutrino mass po… phenomenon 108.76: The proton does not decay 108.76 The proton does… pending : ch:10-renormalization-group@pending-1 pending pending : ch:10-renormalization-group@pending-2 pending pending : ch:10-renormalization-group@pending-3 pending pending : ch:10-renormalization-group@pending-4 pending pending : ch:10-renormalization-group@pending-5 pending pending : ch:10-renormalization-group@pending-6 pending The chain of The Renormalization Group: 47 of 78 objects, read left to right from what the chapter assumes to what tests it. Solid lines are declared logical edges, dashed ones were inferred from the structure of the source. Click any node to open its own chain.