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docs: Notes for normal-ordered Wicks

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jstoobysmith 2025-02-07 09:56:37 +00:00
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5
HepLean/PerturbationTheory/WickContraction/Sign/Join.lean
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@ -429,6 +429,11 @@ lemma join_sign {φs : List 𝓕.FieldOp} (φsΛ : WickContraction φs.length)
(join φsΛ φsucΛ).sign = φsΛ.sign * φsucΛ.sign := by
exact join_sign_induction φsΛ φsucΛ hc (φsΛ).1.card rfl
/-- For a list `φs` of `𝓕.FieldOp`, a Wick contraction `φsΛ` of `φs`,
and a Wick contraction `φsucΛ` of `[φsΛ]ᵘᶜ`,
`(join φsΛ φsucΛ).sign • (join φsΛ φsucΛ).timeContract` is equal to the product of
- `φsΛ.sign • φsΛ.timeContract` and
- `φsucΛ.sign • φsucΛ.timeContract`. -/
lemma join_sign_timeContract {φs : List 𝓕.FieldOp} (φsΛ : WickContraction φs.length)
(φsucΛ : WickContraction [φsΛ]ᵘᶜ.length) :
(join φsΛ φsucΛ).sign • (join φsΛ φsucΛ).timeContract.1 =