feat: More notes for Wick's theorem

HepLean/PerturbationTheory/FieldOpAlgebra/NormalOrder/Lemmas.lean

@@ -217,6 +217,9 @@ lemma anPart_mul_normalOrder_ofFieldOpList_eq_superCommute (φ : 𝓕.FieldOp)
 -/
 
 /--
+For a `CrAnFieldOp` `φ` and a list of `CrAnFieldOp`s `φs`, the following is true
+`[φ, 𝓝(φ₀…φₙ)]ₛ = ∑ i, 𝓢(φ, φ₀…φᵢ₋₁) • [φ, φᵢ]ₛ * 𝓝(φ₀…φᵢ₋₁φᵢ₊₁…φₙ)`.
+
 The proof of this result ultimetly depends on
 - `superCommuteF_ofCrAnListF_ofFieldOpListF_eq_sum`
 - `normalOrderSign_eraseIdx`

HepLean/PerturbationTheory/FieldSpecification/CrAnFieldOp.lean

@@ -106,4 +106,10 @@ scoped[FieldSpecification] notation 𝓕 "|>ₛ" φ => FieldStatistic.ofList
 scoped[FieldSpecification] infixl:80 "|>ᶜ" =>
     crAnFieldOpToCreateAnnihilate
 
+remark notation_remark := "When working with a field specification `𝓕` we will use
+some notation within doc-strings and in code. The main notation used is:
+- In docstrings when field statistics occur in exchange signs we may drop the `𝓕 |>ₛ`.
+- In docstrings we will often write lists of `FieldOp` or `CrAnFieldOp` `φs` as e.g. `φ₀…φₙ`,
+  which should be interpreted within the context in which it appears."
+
 end FieldSpecification

HepLean/PerturbationTheory/FieldSpecification/TimeOrder.lean

@@ -191,7 +191,14 @@ lemma timeOrderList_eq_maxTimeField_timeOrderList (φ : 𝓕.FieldOp) (φs : Lis
 
 -/
 
-/-- The time ordering relation on CrAnFieldOp. -/
+/-- For a field specification `𝓕`,  `𝓕.crAnTimeOrderRel` is time ordering relation on
+  `𝓕.CrAnFieldOp` defined to put those field operators with greatest time to the left on
+  ordering a list. Thus `𝓕.crAnTimeOrderRel φ₀ φ₁` is true if and only if one of the following is
+  true
+- `φ₀` is an outgoing asymptotic creation and annihilation field operator
+- `φ₁` is an incoming asymptotic creation and annihilation field operator
+- `φ₀` and `φ₁` are both position operators where `φ₀` occurs at a time greater then or equal to
+  that of `φ₁`. -/
 def crAnTimeOrderRel (a b : 𝓕.CrAnFieldOp) : Prop := 𝓕.timeOrderRel a.1 b.1
 
 /-- The relation `crAnTimeOrderRel` is decidable, but not computablly so due to