proposition 113.3 Degrees of freedom before and after

Rests on

• depends_on equation 104.23 eq:ewh-unitary-gauge ¶
• depends_on proposition 26.34 Proca constraints are second class ¶
  • depends_on definition 26.12 First and second class ¶
    • depends_on definition 26.11 The final constraint set ¶
      • depends_on proposition 26.10 The four outcomes ¶
        • depends_on definition 26.9 Consistency conditions ¶
        • depends_on remark 26.7 The regularity assumption, stated once ¶
        • proves proof ch:09-constrained-hamiltonian-dynamics@proof-3 ¶
      • depends_on remark 26.7 The regularity assumption, stated once ¶ ↺
    • depends_on definition 22.29 Poisson bracket ¶
      • depends_on definition 7.97 Partial derivative; gradient ¶
        • depends_on definition 7.26 Derivative of a function at a point ¶
        • depends_on definition 5.15 Basis ¶
      • depends_on definition 22.14 Phase-space coordinate transformation ¶
        • depends_on definition 22.2 Hamiltonian ¶
  • depends_on proposition 26.32 Constraint structure of the free Maxwell field ¶
    • depends_on proposition 26.10 The four outcomes ¶ ↺
    • depends_on proposition 26.5 Primary constraints ¶
      • depends_on definition 26.3 Singular Lagrangian ¶
        • depends_on equation 22.2 eq:ham-hessian ¶
        • depends_on proposition 22.3 Invertibility of the Legendre map ¶
      • depends_on remark 26.4 The constant-rank theorem is owed by Part II ¶
      • proves proof ch:09-constrained-hamiltonian-dynamics@proof-1 ¶
    • depends_on theorem 26.17 Counting the physical degrees of freedom ¶
      • depends_on proposition 26.19 Second-class constraints come in pairs ¶
        • depends_on definition 26.12 First and second class ¶ ↺
        • depends_on proposition 5.119 Normal form of a non-degenerate antisymmetric form ¶
        • proves proof ch:09-constrained-hamiltonian-dynamics@proof-7 ¶
      • depends_on remark 26.18 The Frobenius theorem is owed by Part II ¶
      • depends_on theorem 26.14 First-class constraints generate gauge transformations ¶
        • depends_on definition 26.8 Total Hamiltonian ¶
        • depends_on proposition 26.10 The four outcomes ¶ ↺
        • proves proof ch:09-constrained-hamiltonian-dynamics@proof-5 ¶
      • proves proof ch:09-constrained-hamiltonian-dynamics@proof-6 ¶
    • proves proof ch:09-constrained-hamiltonian-dynamics@proof-13 ¶
  • depends_on theorem 26.17 Counting the physical degrees of freedom ¶ ↺
  • proves proof ch:09-constrained-hamiltonian-dynamics@proof-14 ¶
• depends_on theorem 104.25 The breaking pattern ¶
  • depends_on equation 104.27 eq:ewh-scalar-lagrangian ¶
  • depends_on theorem 104.17 Goldstone's theorem, tree level ¶
    • depends_on definition 104.14 Spontaneous breaking ¶
    • proves proof ch:06-electroweak-higgs@proof-7 ¶
  • depends_on theorem 104.22 Kibble: the gauge-boson mass matrix ¶
    • depends_on theorem 104.19 The abelian Higgs mechanism ¶
      • depends_on equation 104.16 eq:ewh-goldstone-expansion ¶
      • depends_on equation 104.6 eq:ewh-longitudinal ¶
      • depends_on equation 100.8 eq:qed-gauge-transformation ¶
      • proves proof ch:06-electroweak-higgs@proof-8 ¶
    • depends_on theorem 104.17 Goldstone's theorem, tree level ¶ ↺
    • proves proof ch:06-electroweak-higgs@proof-10 ¶
  • proves proof ch:06-electroweak-higgs@proof-11 ¶
• proves proof ch:15-exp-higgs-discovery@proof-1 ¶

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