proposition 26.24 The Faddeev–Popov determinant

open in the book · parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:805 · p. 908

Rests on

depends_on definition 26.23 Gauge conditions ¶
- depends_on definition 26.20 Dirac bracket ¶
  - 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 26.19 Second-class constraints come in pairs ¶
    - depends_on definition 26.12 First and second class ¶
      - depends_on definition 26.11 The final constraint set ¶
      - depends_on definition 22.29 Poisson bracket ¶ ↺
    - 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 theorem 26.17 Counting the physical degrees of freedom ¶
  - depends_on proposition 26.19 Second-class constraints come in pairs ¶ ↺
  - 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 ¶
      - 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 ¶
    - proves proof ch:09-constrained-hamiltonian-dynamics@proof-5 ¶
  - proves proof ch:09-constrained-hamiltonian-dynamics@proof-6 ¶
depends_on proposition 26.19 Second-class constraints come in pairs ¶ ↺
proves proof ch:09-constrained-hamiltonian-dynamics@proof-10 ¶

Supports

depends_on remark 26.26 What the factor is doing ¶

Neighborhood

Every logical edge within two steps of this node.

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partly declared
a check failed
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Edges

type	direction	node	provenance	where
`cites`	→	Feynman diagrams for the Yang-Mills field	derived	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:817
`depends_on`	→	Gauge conditions	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:820
`depends_on`	→	Second-class constraints come in pairs	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:820
`depends_on`	←	What the factor is doing	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:1004
`proves`	←	ch:09-constrained-hamiltonian-dynamics@proof-10	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:823