definition A.647 Koszul–Tate differential

open in the book · appendices/A-long-proofs.tex:31582 · p. 3107

ground object -- no derivation owed

Rests on

depends_on equation 26.16 eq:cd-first-class-algebra ¶
depends_on notation A.646 Gradings and brackets ¶
- depends_on definition 26.50 The BRST charge ¶
  - depends_on equation 26.16 eq:cd-first-class-algebra ¶ ↺
  - depends_on postulate 26.47 Dirac quantization ¶
    - depends_on postulate 25.27 Dirac's correspondence rule ¶
      - depends_on equation 22.41 eq:ham-poisson-bracket ¶
      - depends_on theorem 25.3 The bracket is a Lie bracket ¶
    - depends_on theorem 26.21 Properties of the Dirac bracket ¶
      - depends_on definition 26.20 Dirac bracket ¶
      - depends_on definition 26.8 Total Hamiltonian ¶
      - depends_on proposition 26.19 Second-class constraints come in pairs ¶
      - proves proof ch:09-constrained-hamiltonian-dynamics@proof-8 ¶
      - proves proof ch:09-constrained-hamiltonian-dynamics@prooflink-1 ¶
    - 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 ¶
- depends_on equation 26.97 eq:cd-brst-charge ¶
- depends_on equation 26.16 eq:cd-first-class-algebra ¶ ↺

Supports

depends_on lemma A.651 Acyclicity of $\delta$ ¶
- depends_on proposition A.655 Uniqueness up to a canonical transformation ¶
- depends_on theorem A.653 Existence of a nilpotent BRST charge ¶
  - depends_on proposition A.655 Uniqueness up to a canonical transformation ¶ ↺
depends_on lemma A.648 $\delta$ is the ghost bracket with $\Omega_{(0)}$, and $\delta^{2}=0$ ¶
- depends_on lemma A.652 Nilpotency, order by order ¶
  - depends_on proposition A.654 The Yang–Mills case ¶
  - depends_on proposition A.655 Uniqueness up to a canonical transformation ¶ ↺
  - depends_on theorem A.653 Existence of a nilpotent BRST charge ¶ ↺

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	eq:cd-first-class-algebra	declared	appendices/A-long-proofs.tex:31592
`depends_on`	→	Gradings and brackets	declared	appendices/A-long-proofs.tex:31592
`depends_on`	←	Acyclicity of $\delta$	declared	appendices/A-long-proofs.tex:31686
`depends_on`	←	$\delta$ is the ghost bracket with $\Omega_{(0)}$, and $\delta^{2}=0$	declared	appendices/A-long-proofs.tex:31599