proposition 26.37 Constraint structure of Yang–Mills theory

Rests on

• depends_on notation 26.36 Gauge fields and their SI dimensions ¶
  • depends_on equation 102.24 eq:qcd-field-strength ¶
  • depends_on notation 26.28 Field systems ¶
    • 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 notation 26.1 Weak and strong equality ¶
      • depends_on definition 22.29 Poisson bracket ¶ ↺
      • depends_on notation 22.1 not:ham-indices ¶
  • depends_on notation 102.18 Colour fields and their SI dimensions ¶
• depends_on proposition 26.13 The first-class functions close ¶
  • 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 equation 22.46 eq:ham-jacobi ¶
  • depends_on remark 26.7 The regularity assumption, stated once ¶ ↺
  • proves proof ch:09-constrained-hamiltonian-dynamics@proof-4 ¶
• 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 corollary A.292 Inverse function theorem ¶
        • depends_on equation 21.43 eq:lag-generalized-momentum ¶
        • proves proof ch:05-hamiltonian-mechanics@proof-1 ¶
    • 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 ¶
        • depends_on definition 5.110 Bilinear map ¶
        • depends_on definition 5.113 Non-degenerate form ¶
        • depends_on definition 5.111 Symmetric and antisymmetric forms ¶
        • depends_on equation 5.139 eq:lin-bilinear-congruence ¶
        • proves proof ch:03-linear-algebra-representations@proof-54 ¶
      • 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 definition 22.29 Poisson bracket ¶ ↺
        • depends_on proposition 26.6 The canonical Hamiltonian is defined on the constraint surface ¶
      • 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 ¶
• proves proof ch:09-constrained-hamiltonian-dynamics@proof-15 ¶

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