proposition 106.88 The obstruction

open in the book · parts/11-qft-standard-model/08-path-integral-quantization.tex:4145 · p. 2201

Rests on

depends_on lemma 106.86 A shift of a divergent integral leaves a surface term ¶
- depends_on theorem 7.133 Gauss ¶
  - depends_on definition 7.127 Simple regions ¶
    - depends_on definition 7.98 Functions of class $C^{1}$ ¶
      - depends_on definition 7.20 Continuity at a point ¶
      - depends_on definition 7.97 Partial derivative; gradient ¶
    - depends_on definition 6.9 Compact set ¶
      - depends_on definition 6.5 Open cover ¶
  - depends_on remark 7.128 What the derivations below take as given ¶
    - depends_on definition 7.125 Multiple integral ¶
      - depends_on axiom 7.1 Completeness of $\R$ ¶
      - depends_on definition 7.39 Darboux sums and the definite integral ¶
    - depends_on theorem 7.40 Continuous functions are integrable ¶
      - depends_on definition 7.39 Darboux sums and the definite integral ¶ ↺
      - depends_on theorem 7.24 Extreme value theorem ¶
      - depends_on theorem 7.25 Heine–Cantor: uniform continuity ¶
      - proves proof ch:05-real-analysis@proof-23 ¶
    - depends_on theorem 7.25 Heine–Cantor: uniform continuity ¶ ↺
  - depends_on theorem 7.43 Fundamental theorem of calculus, II ¶
    - depends_on definition 7.41 Antiderivative ¶
      - depends_on corollary 7.36 cor:ana-mvt-consequences ¶
      - depends_on definition 7.26 Derivative of a function at a point ¶
    - depends_on theorem 7.42 Fundamental theorem of calculus, I ¶
      - depends_on definition 7.26 Derivative of a function at a point ¶ ↺
      - depends_on theorem 7.40 Continuous functions are integrable ¶ ↺
      - depends_on theorem 7.24 Extreme value theorem ¶ ↺
      - proves proof ch:05-real-analysis@proof-24 ¶
    - proves proof ch:05-real-analysis@proof-25 ¶
  - proves proof ch:05-real-analysis@proof-79 ¶
- proves proof ch:08-path-integral-quantization@proof-59 ¶
depends_on theorem 100.17 Superficial degree of divergence ¶
- depends_on equation 100.23 eq:qed-fermion-propagator ¶
- depends_on equation 100.17 eq:qed-photon-propagator ¶
- depends_on theorem 100.10 Furry ¶
  - depends_on definition 100.9 Charge conjugation on the Dirac field ¶
  - depends_on equation 100.20 eq:qed-C-matrix ¶
  - proves proof ch:02-qed-renormalization@proof-5 ¶
- proves proof ch:02-qed-renormalization@proof-8 ¶
proves proof ch:08-path-integral-quantization@proof-60 ¶

Supports

depends_on theorem 106.95 The cancellation condition ¶
- depends_on proposition 104.53 One generation is anomaly free ¶
- depends_on proposition 106.96 The Standard Model cancels, and only with three colours ¶

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`	→	A shift of a divergent integral leaves a surface term	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:4153
`depends_on`	→	Superficial degree of divergence	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:4153
`depends_on`	←	The cancellation condition	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:4647
`proves`	←	ch:08-path-integral-quantization@proof-60	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:4156