lemma 100.27 Wick rotation

open in the book · parts/11-qft-standard-model/02-qed-renormalization.tex:1357 · p. 1914

Rests on

depends_on equation 100.23 eq:qed-fermion-propagator ¶
depends_on theorem 8.12 Cauchy ¶
- depends_on equation 8.5 eq:cpx-cr ¶
- depends_on theorem 7.131 Green ¶
  - 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-77 ¶
- proves proof ch:06-complex-analysis@proof-7 ¶
proves proof ch:02-qed-renormalization@proof-16 ¶

Supports

depends_on lemma 100.28 The $d$-dimensional loop integral ¶
- depends_on proposition 106.45 One-loop effective potential ¶
- depends_on theorem 100.35 One-loop electron self-energy ¶
  - depends_on phenomenon 100.66 The Lamb shift ¶
- depends_on theorem 100.31 One-loop vacuum polarization ¶
  - depends_on phenomenon 100.69 Light scatters off light ¶

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
`depends_on`	→	eq:qed-fermion-propagator	declared	parts/11-qft-standard-model/02-qed-renormalization.tex:1373
`depends_on`	→	Cauchy	declared	parts/11-qft-standard-model/02-qed-renormalization.tex:1373
`depends_on`	←	The $d$-dimensional loop integral	declared	parts/11-qft-standard-model/02-qed-renormalization.tex:1427
`proves`	←	ch:02-qed-renormalization@proof-16	declared	parts/11-qft-standard-model/02-qed-renormalization.tex:1376