lemma A.652 Nilpotency, order by order

open in the book · appendices/A-long-proofs.tex:31768 · p. 3109

Rests on

depends_on equation 26.98 eq:cd-brst-nilpotent ¶
depends_on lemma A.648 $\delta$ is the ghost bracket with $\Omega_{(0)}$, and $\delta^{2}=0$ ¶
- depends_on definition A.647 Koszul–Tate differential ¶
  - 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 equation 26.97 eq:cd-brst-charge ¶
    - depends_on equation 26.16 eq:cd-first-class-algebra ¶ ↺
- depends_on equation A.1034 eq:app-brst-existence-first-two ¶
- depends_on equation A.1030 eq:app-brst-existence-graded ¶
- proves proof app:A-long-proofs@proof-389 ¶
depends_on notation A.646 Gradings and brackets ¶ ↺
proves proof app:A-long-proofs@proof-392 ¶

Supports

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 ¶
- depends_on proposition A.655 Uniqueness up to a canonical transformation ¶ ↺

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-brst-nilpotent	declared	appendices/A-long-proofs.tex:31796
`depends_on`	→	$\delta$ is the ghost bracket with $\Omega_{(0)}$, and $\delta^{2}=0$	declared	appendices/A-long-proofs.tex:31796
`depends_on`	→	Gradings and brackets	declared	appendices/A-long-proofs.tex:31796
`depends_on`	←	The Yang–Mills case	declared	appendices/A-long-proofs.tex:31932
`depends_on`	←	Uniqueness up to a canonical transformation	declared	appendices/A-long-proofs.tex:31981
`depends_on`	←	Existence of a nilpotent BRST charge	declared	appendices/A-long-proofs.tex:31867
`proves`	←	app:A-long-proofs@proof-392	declared	appendices/A-long-proofs.tex:31800