theorem 100.31 One-loop vacuum polarization

open in the book · parts/11-qft-standard-model/02-qed-renormalization.tex:1534 · p. 1916

Rests on

depends_on lemma 100.28 The $d$-dimensional loop integral ¶
- depends_on equation 17.42 eq:ft-gaussian ¶
- depends_on equation 17.109 eq:ft-mellin-gamma ¶
- depends_on lemma 100.27 Wick rotation ¶
  - 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 remark 7.128 What the derivations below take as given ¶
      - depends_on theorem 7.43 Fundamental theorem of calculus, II ¶
      - proves proof ch:05-real-analysis@proof-77 ¶
    - proves proof ch:06-complex-analysis@proof-7 ¶
  - proves proof ch:02-qed-renormalization@proof-16 ¶
- proves proof ch:02-qed-renormalization@proof-17 ¶
depends_on lemma 100.23 Trace theorems ¶
- depends_on equation 100.5 eq:qed-free-dirac ¶
- proves proof ch:02-qed-renormalization@proof-12 ¶
depends_on proposition 100.14 The Feynman rules of QED in SI form ¶
- depends_on equation 100.2 eq:qed-action ¶
- depends_on proposition 100.8 The photon propagator ¶
  - depends_on equation 100.2 eq:qed-action ¶ ↺
  - depends_on equation 100.16 eq:qed-gauge-fixing-term ¶
  - depends_on equation 100.15 eq:qed-photon-kernel ¶
  - proves proof ch:02-qed-renormalization@proof-4 ¶
- depends_on theorem 100.5 The gauge principle ¶
  - depends_on equation 100.6 eq:qed-current ¶
  - depends_on equation 100.5 eq:qed-free-dirac ¶ ↺
  - proves proof ch:02-qed-renormalization@proof-1 ¶
- proves proof ch:02-qed-renormalization@proof-7 ¶
proves proof ch:02-qed-renormalization@proof-19 ¶

Supports

depends_on phenomenon 100.69 Light scatters off light ¶

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`	→	The $d$-dimensional loop integral	declared	parts/11-qft-standard-model/02-qed-renormalization.tex:1552
`depends_on`	→	Trace theorems	declared	parts/11-qft-standard-model/02-qed-renormalization.tex:1552
`depends_on`	→	The Feynman rules of QED in SI form	declared	parts/11-qft-standard-model/02-qed-renormalization.tex:1552
`depends_on`	←	Light scatters off light	declared	parts/11-qft-standard-model/02-qed-renormalization.tex:3342
`proves`	←	ch:02-qed-renormalization@proof-19	declared	parts/11-qft-standard-model/02-qed-renormalization.tex:1555