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refactor: improve docs

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jstoobysmith 2025-01-24 11:09:25 +00:00
parent eeacdef74e
commit 2490535569
6 changed files with 126 additions and 57 deletions
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7
HepLean/PerturbationTheory/WickContraction/TimeContract.lean
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@ -18,7 +18,7 @@ namespace WickContraction
variable {n : ℕ} (c : WickContraction n)
open HepLean.List
/-- Given a Wick contraction `c` associated with a list `φs`, the
/-- Given a Wick contraction `φsΛ` associated with a list `φs`, the
product of all time-contractions of pairs of contracted elements in `φs`,
as a member of the center of `𝓞.A`. -/
noncomputable def timeContract (𝓞 : 𝓕.ProtoOperatorAlgebra) {φs : List 𝓕.States}
@ -28,6 +28,11 @@ noncomputable def timeContract (𝓞 : 𝓕.ProtoOperatorAlgebra) {φs : List
(φs.get (φsΛ.fstFieldOfContract a)) (φs.get (φsΛ.sndFieldOfContract a)),
𝓞.timeContract_mem_center _ _⟩
/-- For `φsΛ` a Wick contraction for `φs`, the time contraction `(φsΛ ↩Λ φ i none).timeContract 𝓞`
is equal to `φsΛ.timeContract 𝓞`.
This result follows from the fact that `timeContract` only depends on contracted pairs,
and `(φsΛ ↩Λ φ i none)` has the 'same' contracted pairs as `φsΛ`. -/
@[simp]
lemma timeContract_insertAndContract_none (𝓞 : 𝓕.ProtoOperatorAlgebra) (φ : 𝓕.States) (φs : List 𝓕.States)
(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) :