proposition 106.45 One-loop effective potential

open in the book · parts/11-qft-standard-model/08-path-integral-quantization.tex:2194 · p. 2180

Rests on

depends_on equation 106.59 eq:pathint-effective-potential-def ¶
depends_on equation 106.58 eq:pathint-gamma-one-loop ¶
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 ¶
proves proof ch:08-path-integral-quantization@proof-32 ¶

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type	direction	node	provenance	where
`depends_on`	→	eq:pathint-effective-potential-def	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:2208
`depends_on`	→	eq:pathint-gamma-one-loop	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:2208
`depends_on`	→	The $d$-dimensional loop integral	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:2208
`proves`	←	ch:08-path-integral-quantization@proof-32	declared	parts/11-qft-standard-model/08-path-integral-quantization.tex:2212