docs: Field specification docs

HepLean/PerturbationTheory/CreateAnnihilate.lean

@@ -10,7 +10,9 @@ import Mathlib.Algebra.BigOperators.Group.Finset
 
 -/
 
-/-- The type specifing whether an operator is a creation or annihilation operator. -/
+/-- The type `CreateAnnihilate` is the type containing two elements `create` and `annihilate`.
+  This type is used to specify if an operator is a creation or annihilation operator
+  or the sum thereof or intergral thereover etc. -/
 inductive CreateAnnihilate where
   | create : CreateAnnihilate
   | annihilate : CreateAnnihilate

HepLean/PerturbationTheory/FieldOpAlgebra/Basic.lean

@@ -512,18 +512,18 @@ def anPart (φ : 𝓕.FieldOp) : 𝓕.FieldOpAlgebra := ι (anPartF φ)
 lemma anPart_eq_ι_anPartF (φ : 𝓕.FieldOp) : anPart φ = ι (anPartF φ) := rfl
 
 @[simp]
-lemma anPart_negAsymp (φ : 𝓕.asymptoticDOF × (Fin 3 → ℝ)) :
+lemma anPart_negAsymp (φ : (Σ f, 𝓕.AsymptoticLabel f) × (Fin 3 → ℝ)) :
     anPart (FieldOp.inAsymp φ) = 0 := by
   simp [anPart, anPartF]
 
 @[simp]
-lemma anPart_position (φ : 𝓕.positionDOF × SpaceTime) :
+lemma anPart_position (φ : (Σ f, 𝓕.PositionLabel f) × SpaceTime) :
     anPart (FieldOp.position φ) =
     ofCrAnFieldOp ⟨FieldOp.position φ, CreateAnnihilate.annihilate⟩ := by
   simp [anPart, ofCrAnFieldOp]
 
 @[simp]
-lemma anPart_posAsymp (φ : 𝓕.asymptoticDOF × (Fin 3 → ℝ)) :
+lemma anPart_posAsymp (φ : (Σ f, 𝓕.AsymptoticLabel f) × (Fin 3 → ℝ)) :
     anPart (FieldOp.outAsymp φ) = ofCrAnFieldOp ⟨FieldOp.outAsymp φ, ()⟩ := by
   simp [anPart, ofCrAnFieldOp]
 
@@ -533,18 +533,18 @@ def crPart (φ : 𝓕.FieldOp) : 𝓕.FieldOpAlgebra := ι (crPartF φ)
 lemma crPart_eq_ι_crPartF (φ : 𝓕.FieldOp) : crPart φ = ι (crPartF φ) := rfl
 
 @[simp]
-lemma crPart_negAsymp (φ : 𝓕.asymptoticDOF × (Fin 3 → ℝ)) :
+lemma crPart_negAsymp (φ : (Σ f, 𝓕.AsymptoticLabel f) × (Fin 3 → ℝ)) :
     crPart (FieldOp.inAsymp φ) = ofCrAnFieldOp ⟨FieldOp.inAsymp φ, ()⟩ := by
   simp [crPart, ofCrAnFieldOp]
 
 @[simp]
-lemma crPart_position (φ : 𝓕.positionDOF × SpaceTime) :
+lemma crPart_position (φ : (Σ f, 𝓕.PositionLabel f) × SpaceTime) :
     crPart (FieldOp.position φ) =
     ofCrAnFieldOp ⟨FieldOp.position φ, CreateAnnihilate.create⟩ := by
   simp [crPart, ofCrAnFieldOp]
 
 @[simp]
-lemma crPart_posAsymp (φ : 𝓕.asymptoticDOF × (Fin 3 → ℝ)) :
+lemma crPart_posAsymp (φ : (Σ f, 𝓕.AsymptoticLabel f) × (Fin 3 → ℝ)) :
     crPart (FieldOp.outAsymp φ) = 0 := by
   simp [crPart]
 

HepLean/PerturbationTheory/FieldOpFreeAlgebra/Basic.lean

@@ -131,18 +131,18 @@ def crPartF : 𝓕.FieldOp → 𝓕.FieldOpFreeAlgebra := fun φ =>
   | FieldOp.outAsymp _ => 0
 
 @[simp]
-lemma crPartF_negAsymp (φ : 𝓕.asymptoticDOF × (Fin 3 → ℝ)) :
+lemma crPartF_negAsymp (φ : (Σ f, 𝓕.AsymptoticLabel f) × (Fin 3 → ℝ)) :
     crPartF (FieldOp.inAsymp φ) = ofCrAnOpF ⟨FieldOp.inAsymp φ, ()⟩ := by
   simp [crPartF]
 
 @[simp]
-lemma crPartF_position (φ : 𝓕.positionDOF × SpaceTime) :
+lemma crPartF_position (φ : (Σ f, 𝓕.PositionLabel f) × SpaceTime) :
     crPartF (FieldOp.position φ) =
     ofCrAnOpF ⟨FieldOp.position φ, CreateAnnihilate.create⟩ := by
   simp [crPartF]
 
 @[simp]
-lemma crPartF_posAsymp (φ : 𝓕.asymptoticDOF × (Fin 3 → ℝ)) :
+lemma crPartF_posAsymp (φ : (Σ f, 𝓕.AsymptoticLabel f) × (Fin 3 → ℝ)) :
     crPartF (FieldOp.outAsymp φ) = 0 := by
   simp [crPartF]
 
@@ -156,18 +156,18 @@ def anPartF : 𝓕.FieldOp → 𝓕.FieldOpFreeAlgebra := fun φ =>
   | FieldOp.outAsymp φ => ofCrAnOpF ⟨FieldOp.outAsymp φ, ()⟩
 
 @[simp]
-lemma anPartF_negAsymp (φ : 𝓕.asymptoticDOF × (Fin 3 → ℝ)) :
+lemma anPartF_negAsymp (φ : (Σ f, 𝓕.AsymptoticLabel f) × (Fin 3 → ℝ)) :
     anPartF (FieldOp.inAsymp φ) = 0 := by
   simp [anPartF]
 
 @[simp]
-lemma anPartF_position (φ : 𝓕.positionDOF × SpaceTime) :
+lemma anPartF_position (φ : (Σ f, 𝓕.PositionLabel f) × SpaceTime) :
     anPartF (FieldOp.position φ) =
     ofCrAnOpF ⟨FieldOp.position φ, CreateAnnihilate.annihilate⟩ := by
   simp [anPartF]
 
 @[simp]
-lemma anPartF_posAsymp (φ : 𝓕.asymptoticDOF × (Fin 3 → ℝ)) :
+lemma anPartF_posAsymp (φ : (Σ f, 𝓕.AsymptoticLabel f) × (Fin 3 → ℝ)) :
     anPartF (FieldOp.outAsymp φ) = ofCrAnOpF ⟨FieldOp.outAsymp φ, ()⟩ := by
   simp [anPartF]
 

HepLean/PerturbationTheory/FieldSpecification/Basic.lean

@@ -29,50 +29,63 @@ These states carry the same field statistic as the field they are derived from.
 
 -/
 
-/-- A field specification is defined as a structure containing the basic data needed to write down
-  position and asymptotic field operators for a theory. It contains:
-  - A type `positionDOF` containing the degree-of-freedom in position-based field
-  operators (excluding space-time position). Thus a sutible (but not unique) choice
-    - Real-scalar fields correspond to a single element of `positionDOF`.
-    - Complex-scalar fields correspond to two elements of `positionDOF`, one for the field and one
-      for its conjugate.
-    - Dirac fermions correspond to eight elements of `positionDOF`. One for each Lorentz index of
-      the field and its conjugate. (These are not all independent)
-    - Weyl fermions correspond to four elements of `positionDOF`. One for each Lorentz index of the
-      field. (These are not all independent)
-  - A type `asymptoticDOF` containing the degree-of-freedom in asymptotic field operators. Thus a
-    sutible (but not unique) choice is
-    - Real-scalar fields correspond to a single element of `asymptoticDOF`.
-    - Complex-scalar fields correspond to two elements of `asymptoticDOF`, one for the field and one
-      for its conjugate.
-    - Dirac fermions correspond to four elements of `asymptoticDOF`, two for each type of spin.
-    - Weyl fermions correspond to two elements of `asymptoticDOF`, one for each spin.
-  - A specification `statisticsPos` on a `positionDOF` is Fermionic or Bosonic.
-  - A specification `statisticsAsym` on a `asymptoticDOF` is Fermionic or Bosonic.
+/--
+The structure `FieldSpecification` is defined to have the following content:
+  - A type `Field` whose elements are the constituent fields of the theory.
+  - For every field `f` in `Field`, a type `PositionLabel f` whose elements label the different
+    position operators associated with the field `f`. For example,
+    - For `f` a *real-scalar field*, `PositionLabel f` will have a unique element.
+    - For `f` a *complex-scalar field*, `PositionLabel f` will have two elements, one for the field
+      operator and one for its conjugate.
+    - For `f` a *Dirac fermion*, `PositionLabel f` will have eight elements, one for each Lorentz
+      index of the field and its conjugate.
+    - For `f` a *Weyl fermion*, `PositionLabel f` will have four elements, one for each Lorentz
+      index of the field and its conjugate.
+  - For every field `f` in `Field`, a type `AsymptoticLabel f` whose elements label the different
+    asymptotic based field operators associated with the field `f`. For example,
+    - For `f` a *real-scalar field*, `AsymptoticLabel f` will have a unique element.
+    - For `f` a *complex-scalar field*, `AsymptoticLabel f` will have two elements, one for the
+      field operator and one for its conjugate.
+    - For `f` a *Dirac fermion*, `AsymptoticLabel f` will have four elements, two for each spin.
+    - For `f` a *Weyl fermion*, `AsymptoticLabel f` will have two elements, one for each spin.
+  - For each field `f` in `Field`, a field statistic `statistic f` which classifying `f` as either
+    `bosonic` or `fermionic`.
 -/
 structure FieldSpecification where
-  /-- Degrees of freedom for position based field operators. -/
-  positionDOF : Type
-  /-- Degrees of freedom for asymptotic based field operators. -/
-  asymptoticDOF : Type
-  /-- The specification if the `positionDOF` are Fermionic or Bosonic. -/
-  statisticsPos : positionDOF → FieldStatistic
-  /-- The specification if the `asymptoticDOF` are Fermionic or Bosonic. -/
-  statisticsAsym : asymptoticDOF → FieldStatistic
+  /-- A type whose elements are the constituent fields of the theory. -/
+  Field : Type
+  /-- For every field `f` in `Field`, the type `PositionLabel f` has elements that label the
+    different position operators associated with the field `f`. -/
+  PositionLabel : Field → Type
+  /-- For every field `f` in `Field`, the type `AsymptoticLabel f` has elements that label
+    the different asymptotic based field operators associated with the field `f`. -/
+  AsymptoticLabel : Field → Type
+  /-- For every field `f` in `Field`, the field statistic `statistic f` classifies `f` as either
+    `bosonic` or `fermionic`. -/
+  statistic : Field → FieldStatistic
 
 namespace FieldSpecification
 variable (𝓕 : FieldSpecification)
 
 /-- For a field specification `𝓕`, the type `𝓕.FieldOp` is defined such that every element of
   `FieldOp` corresponds either to:
-- an incoming asymptotic field operator `.inAsymp` specified by a field and a `3`-momentum.
-- an position operator `.position` specified by a field and a point in spacetime.
-- an outgoing asymptotic field operator `.outAsymp` specified by a field and a `3`-momentum.
+- an incoming asymptotic field operator `.inAsymp` which is specified by
+  a field `f` in `𝓕.Field`, an element of `AsymptoticLabel f` (which specifies exactly
+  which asymptotic field operator associated with `f`) and a `3`-momentum.
+- an position operator `.position` which is specified by
+  a field `f` in `𝓕.Field`, an element of `PositionLabel f` (which specifies exactly
+  which position field operator associated with `f`) and a element of `SpaceTime`.
+- an outgoing asymptotic field operator `.outAsymp` which is specified by
+  a field `f` in `𝓕.Field`, an element of `AsymptoticLabel f` (which specifies exactly
+  which asymptotic field operator associated with `f`) and a `3`-momentum.
+
+Note the use of `3`-momentum here rather then `4`-momentum. This is because the asymptotic states
+have on-shell momenta.
 -/
 inductive FieldOp (𝓕 : FieldSpecification) where
-  | inAsymp : 𝓕.asymptoticDOF × (Fin 3 → ℝ) → 𝓕.FieldOp
-  | position : 𝓕.positionDOF × SpaceTime → 𝓕.FieldOp
-  | outAsymp : 𝓕.asymptoticDOF × (Fin 3 → ℝ) → 𝓕.FieldOp
+  | inAsymp : (Σ f, 𝓕.AsymptoticLabel f) × (Fin 3 → ℝ) → 𝓕.FieldOp
+  | position : (Σ f, 𝓕.PositionLabel f) × SpaceTime → 𝓕.FieldOp
+  | outAsymp : (Σ f, 𝓕.AsymptoticLabel f) × (Fin 3 → ℝ) → 𝓕.FieldOp
 
 
 /-- The bool on `FieldOp` which is true only for position field operator. -/
@@ -80,22 +93,34 @@ def statesIsPosition : 𝓕.FieldOp → Bool
   | FieldOp.position _ => true
   | _ => false
 
-/-- The statistics associated to a field operator. -/
-def statesStatistic : 𝓕.FieldOp → FieldStatistic := fun f =>
-  match f with
-  | FieldOp.inAsymp (a, _) => 𝓕.statisticsAsym a
-  | FieldOp.position (a, _) => 𝓕.statisticsPos a
-  | FieldOp.outAsymp (a, _) => 𝓕.statisticsAsym a
+/-- For a field specification `𝓕`, `𝓕.fieldOpToField` is defined to take field operators
+  to their underlying field. -/
+def fieldOpToField : 𝓕.FieldOp → 𝓕.Field
+  | FieldOp.inAsymp (f, _) => f.1
+  | FieldOp.position (f, _) => f.1
+  | FieldOp.outAsymp (f, _) => f.1
 
-/-- The field statistics associated with a field operator. -/
-scoped[FieldSpecification] notation 𝓕 "|>ₛ" φ => statesStatistic 𝓕 φ
+/-- For a field specification `𝓕`, and an element `φ` of `𝓕.FieldOp`.
+  The field statistic `fieldOpStatistic φ` is defined to be the statistic associated with
+  the field underlying `φ`.
 
-/-- The field statistics associated with a list field operators. -/
+  The following notation is used in relation to `fieldOpStatistic`:
+- For `φ` an element of  `𝓕.FieldOp`, `𝓕 |>ₛ φ` is `fieldOpStatistic φ`.
+- For `φs` a list of  `𝓕.FieldOp`, `𝓕 |>ₛ φs` is the product of `fieldOpStatistic φ` over
+  the list `φs`.
+- For a function `f : Fin n → 𝓕.FieldOp`  and a finset `a` of `Fin n`, `𝓕 |>ₛ ⟨f, a⟩` is the
+  product of `fieldOpStatistic (f i)` for all `i ∈ a`. -/
+def fieldOpStatistic : 𝓕.FieldOp → FieldStatistic :=  𝓕.statistic ∘ 𝓕.fieldOpToField
+
+@[inherit_doc fieldOpStatistic]
+scoped[FieldSpecification] notation 𝓕 "|>ₛ" φ => fieldOpStatistic 𝓕 φ
+
+@[inherit_doc fieldOpStatistic]
 scoped[FieldSpecification] notation 𝓕 "|>ₛ" φ => FieldStatistic.ofList
-    (statesStatistic 𝓕) φ
+    (fieldOpStatistic 𝓕) φ
 
-/-- The field statistic associated with a finite set-/
+@[inherit_doc fieldOpStatistic]
 scoped[FieldSpecification] notation 𝓕 "|>ₛ" "⟨" f ","a "⟩"=> FieldStatistic.ofFinset
-    (statesStatistic 𝓕) f a
+    (fieldOpStatistic 𝓕) f a
 
 end FieldSpecification

HepLean/PerturbationTheory/FieldSpecification/CrAnFieldOp.lean

@@ -63,14 +63,15 @@ def fieldOpToCreateAnnihilateTypeCongr : {i j : 𝓕.FieldOp} → i = j →
   | _, _, rfl => Equiv.refl _
 
 /--
-For a field specification `𝓕`, the type `𝓕.CrAnFieldOp` is defined such that every element
-corresponds to
-- an incoming asymptotic field operator `.inAsymp` and the unique element of `Unit`,
-  corresponding to the statement that an `inAsymp` state is a creation operator.
-- a position operator `.position` and an element of `CreateAnnihilate`,
-  corresponding to either the creation part or the annihilation part of a position operator.
-- an outgoing asymptotic field operator `.outAsymp` and the unique element of `Unit`,
-  corresponding to the statement that an `outAsymp` state is an annihilation operator.
+For a field specification `𝓕`, elements in `𝓕.CrAnFieldOp`, the type
+of creation and annihilation field operators, corresponds to
+- an incoming asymptotic field operator `.inAsymp` in `𝓕.FieldOp`.
+- a position operator `.position` in `𝓕.FieldOp` and an element of
+  `CreateAnnihilate` specifying the creation or annihilation part of that position operator.
+- an outgoing asymptotic field operator `.outAsymp` in `𝓕.FieldOp`.
+
+Note that the incoming and outgoing asymptotic field operators are implicitly creation and
+annihilation operators respectively.
 -/
 def CrAnFieldOp : Type := Σ (s : 𝓕.FieldOp), 𝓕.fieldOpToCrAnType s
 
@@ -89,15 +90,23 @@ def crAnFieldOpToCreateAnnihilate : 𝓕.CrAnFieldOp → CreateAnnihilate
   | ⟨FieldOp.position _, CreateAnnihilate.annihilate⟩ => CreateAnnihilate.annihilate
   | ⟨FieldOp.outAsymp _, _⟩ => CreateAnnihilate.annihilate
 
-/-- Takes a `CrAnFieldOp` state to its corresponding fields statistic (bosonic or fermionic). -/
-def crAnStatistics : 𝓕.CrAnFieldOp → FieldStatistic :=
-  𝓕.statesStatistic ∘ 𝓕.crAnFieldOpToFieldOp
+/-- For a field specification `𝓕`, and an element `φ` in `𝓕.CrAnFieldOp`, the field
+  statistic `crAnStatistics φ` is defined to be the statistic associated with the field `𝓕.Field`
+  (or equivalently `𝓕.FieldOp`) underlying `φ`.
 
-/-- The field statistic of a `CrAnFieldOp`. -/
+  The following notation is used in relation to `crAnStatistics`:
+  - For `φ` an element of  `𝓕.CrAnFieldOp`, `𝓕 |>ₛ φ` is `crAnStatistics φ`.
+  - For `φs` a list of  `𝓕.CrAnFieldOp`, `𝓕 |>ₛ φs` is the product of `crAnStatistics φ` over
+    the list `φs`.
+-/
+def crAnStatistics : 𝓕.CrAnFieldOp → FieldStatistic :=
+  𝓕.fieldOpStatistic ∘ 𝓕.crAnFieldOpToFieldOp
+
+@[inherit_doc crAnStatistics]
 scoped[FieldSpecification] notation 𝓕 "|>ₛ" φ =>
     (crAnStatistics 𝓕) φ
 
-/-- The field statistic of a list of `CrAnFieldOp`s. -/
+@[inherit_doc crAnStatistics]
 scoped[FieldSpecification] notation 𝓕 "|>ₛ" φ => FieldStatistic.ofList
     (crAnStatistics 𝓕) φ
 
@@ -108,8 +117,14 @@ scoped[FieldSpecification] infixl:80 "|>ᶜ" =>
 
 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."
+- In doc-strings when field statistics occur in exchange signs we may drop the `𝓕 |>ₛ _`.
+- In doc-strings 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.
+
+Some examples:
+- `𝓢(φ, φs)` corresponds to  `𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ φs)`
+- `φ₀…φᵢ₋₁φᵢ₊₁…φₙ` corresponds to a (given) list `φs = φ₀…φₙ` with the element at the `i`th position
+  removed.
+"
 
 end FieldSpecification

HepLean/PerturbationTheory/FieldSpecification/TimeOrder.lean

@@ -126,7 +126,7 @@ lemma timeOrder_maxTimeField (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
   the state of greatest time to the left).
   We pick up a minus sign for every fermion paired crossed. -/
 def timeOrderSign (φs : List 𝓕.FieldOp) : ℂ :=
-  Wick.koszulSign 𝓕.statesStatistic 𝓕.timeOrderRel φs
+  Wick.koszulSign 𝓕.fieldOpStatistic 𝓕.timeOrderRel φs
 
 @[simp]
 lemma timeOrderSign_nil : timeOrderSign (𝓕 := 𝓕) [] = 1 := by
@@ -354,7 +354,7 @@ lemma crAnTimeOrderList_swap_eq_time {φ ψ : 𝓕.CrAnFieldOp}
 lemma koszulSignInsert_crAnTimeOrderRel_crAnSection {φ : 𝓕.FieldOp} {ψ : 𝓕.CrAnFieldOp}
     (h : ψ.1 = φ) : {φs : List 𝓕.FieldOp} → (ψs : CrAnSection φs) →
     Wick.koszulSignInsert 𝓕.crAnStatistics 𝓕.crAnTimeOrderRel ψ ψs.1 =
-    Wick.koszulSignInsert 𝓕.statesStatistic 𝓕.timeOrderRel φ φs
+    Wick.koszulSignInsert 𝓕.fieldOpStatistic 𝓕.timeOrderRel φ φs
   | [], ⟨[], h⟩ => by
     simp [Wick.koszulSignInsert]
   | φ' :: φs, ⟨ψ' :: ψs, h1⟩ => by

HepLean/PerturbationTheory/FieldStatistics/Basic.lean

@@ -26,8 +26,13 @@ namespace FieldStatistic
 
 variable {𝓕 : Type}
 
-/-- Field statistics form a commuative group isomorphic to `ℤ₂` in which `bosonic` is the identity
-  and `fermionic` is the non-trivial element. -/
+/-- The type `FieldStatistic` carries an instance of a commuative group in which
+- `bosonic * bosonic = bosonic`
+- `bosonic * fermionic = fermionic`
+- `fermionic * bosonic = fermionic`
+- `fermionic * fermionic = bosonic`
+
+This group is isomorphic to `ℤ₂`. -/
 @[simp]
 instance : CommGroup FieldStatistic where
   one := bosonic

HepLean/PerturbationTheory/FieldStatistics/ExchangeSign.lean

@@ -24,11 +24,12 @@ namespace FieldStatistic
 
 variable {𝓕 : Type}
 
-/-- The exchange sign is the group homomorphism `FieldStatistic →* FieldStatistic →* ℂ`,
-  which on two field statistics `a` and `b` is defined to be
-  `-1` if both `a` and `b` are `fermionic` and `1` otherwise.
-  It corresponds to the sign that one picks up when swapping fields `φ₁φ₂ → φ₂φ₁` with
-  `φ₁` and `φ₂` of statistics `a` and `b` respectively.
+/-- The exchange sign, `exchangeSign`, is defined as the group homomorphism
+  `FieldStatistic →* FieldStatistic →* ℂ`,
+  for which `exchangeSign a b` is `-1` if both `a` and `b` are `fermionic` and `1` otherwise.
+  The exchange sign is sign one picks up on exchanging an operator or field `φ₁` of statistic `a`
+  with one `φ₂` of statistic `b`, i.e. `φ₁φ₂ → φ₂φ₁`.
+
   The notation `𝓢(a, b)` is used for the exchange sign of `a` and `b`. -/
 def exchangeSign : FieldStatistic →* FieldStatistic →* ℂ where
   toFun a :=

HepLean/PerturbationTheory/WickContraction/Sign/Join.lean

@@ -162,7 +162,7 @@ lemma join_singleton_left_signFinset_eq_filter {φs : List 𝓕.FieldOp}
     left
     rw [join_singleton_signFinset_eq_filter]
   rw [mul_comm]
-  exact (ofFinset_filter_mul_neg 𝓕.statesStatistic _ _ _).symm
+  exact (ofFinset_filter_mul_neg 𝓕.fieldOpStatistic _ _ _).symm
 
 /-- The difference in sign between `φsucΛ.sign` and the direct contribution of `φsucΛ` to
   `(join (singleton h) φsucΛ)`. -/

HepLean/PerturbationTheory/WickContraction/StaticContract.lean

@@ -85,7 +85,7 @@ lemma staticContract_insert_some_of_lt
     · simp
     simp only [smul_smul]
     congr 1
-    have h1 : ofList 𝓕.statesStatistic (List.take (↑(φsΛ.uncontractedIndexEquiv.symm k))
+    have h1 : ofList 𝓕.fieldOpStatistic (List.take (↑(φsΛ.uncontractedIndexEquiv.symm k))
         (List.map φs.get φsΛ.uncontractedList))
         = (𝓕 |>ₛ ⟨φs.get, (Finset.filter (fun x => x < k) φsΛ.uncontracted)⟩) := by
       simp only [ofFinset]

HepLean/PerturbationTheory/WickContraction/TimeContract.lean

@@ -97,7 +97,7 @@ lemma timeContract_insert_some_of_lt
     · simp
     simp only [smul_smul]
     congr 1
-    have h1 : ofList 𝓕.statesStatistic (List.take (↑(φsΛ.uncontractedIndexEquiv.symm k))
+    have h1 : ofList 𝓕.fieldOpStatistic (List.take (↑(φsΛ.uncontractedIndexEquiv.symm k))
         (List.map φs.get φsΛ.uncontractedList))
         = (𝓕 |>ₛ ⟨φs.get, (Finset.filter (fun x => x < k) φsΛ.uncontracted)⟩) := by
       simp only [ofFinset]
@@ -128,7 +128,7 @@ lemma timeContract_insert_some_of_not_lt
   rw [timeContract_of_not_timeOrderRel, timeContract_of_timeOrderRel]
   simp only [instCommGroup.eq_1, Algebra.smul_mul_assoc, smul_smul]
   congr
-  have h1 : ofList 𝓕.statesStatistic (List.take (↑(φsΛ.uncontractedIndexEquiv.symm k))
+  have h1 : ofList 𝓕.fieldOpStatistic (List.take (↑(φsΛ.uncontractedIndexEquiv.symm k))
       (List.map φs.get φsΛ.uncontractedList))
       = (𝓕 |>ₛ ⟨φs.get, (Finset.filter (fun x => x < k) φsΛ.uncontracted)⟩) := by
     simp only [ofFinset]