proposition A.655 Uniqueness up to a canonical transformation

Rests on

• depends_on lemma A.651 Acyclicity of $\delta$ ¶
  • 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 lemma A.650 Flattening the constraints ¶
    • depends_on remark 26.4 The constant-rank theorem is owed by Part II ¶
    • depends_on remark 26.7 The regularity assumption, stated once ¶
    • depends_on theorem A.286 Implicit function theorem ¶
      • depends_on definition 7.99 Differentiability at a point ¶
        • depends_on definition 7.16 Limit ¶
        • depends_on definition 5.37 Linear transformation ¶
        • depends_on equation 6.12 eq:top-euclidean-metric ¶
      • depends_on proposition 7.104 Chain rule in several variables ¶
        • depends_on definition 7.13 Composite function ¶
        • depends_on definition 7.99 Differentiability at a point ¶ ↺
        • depends_on definition 7.102 Differential of a function ¶
        • proves proof ch:05-real-analysis@proof-63 ¶
      • depends_on theorem 7.100 $C^{1}$ implies differentiable ¶
        • depends_on definition 7.98 Functions of class $C^{1}$ ¶
        • depends_on definition 7.99 Differentiability at a point ¶ ↺
        • depends_on theorem 7.35 Mean value theorem ¶
        • proves proof ch:05-real-analysis@proof-62 ¶
      • proves proof app:A-long-proofs@proof-185 ¶
    • proves proof app:A-long-proofs@proof-390 ¶
  • depends_on remark A.649 The regularity hypothesis, in the form the proof needs ¶
  • proves proof app:A-long-proofs@proof-391 ¶
• depends_on lemma A.652 Nilpotency, order by order ¶
  • 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 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 ¶
• depends_on theorem A.653 Existence of a nilpotent BRST charge ¶
  • depends_on equation 26.16 eq:cd-first-class-algebra ¶ ↺
  • depends_on lemma A.651 Acyclicity of $\delta$ ¶ ↺
  • depends_on lemma A.652 Nilpotency, order by order ¶ ↺
  • proves proof app:A-long-proofs@proof-393 ¶
• proves proof app:A-long-proofs@proof-395 ¶

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