refactor: Some properties of field specifications (#285)

* refactor: Fix field struct defn.

* rename: FieldStruct to FieldSpecification

* feat: Add examples of field specifications

* docs: Slight improvement of module docs

HepLean/PerturbationTheory/Algebras/CrAnAlgebra/Basic.lean

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Tooby-Smith
 -/
 import HepLean.PerturbationTheory.Algebras.StateAlgebra.Basic
-import HepLean.PerturbationTheory.FieldStruct.CrAnSection
+import HepLean.PerturbationTheory.FieldSpecification.CrAnSection
 /-!
 
 # Creation and annihlation free-algebra
@@ -31,15 +31,15 @@ super commutation relations between creation and annihilation operators.
 
 -/
 
-namespace FieldStruct
-variable {𝓕 : FieldStruct}
+namespace FieldSpecification
+variable {𝓕 : FieldSpecification}
 
 /-- The creation and annihlation free-algebra.
   The free algebra generated by `CrAnStates`,
   that is a position based states or assymptotic states with a specification of
   whether the state is a creation or annihlation state.
   As a module `CrAnAlgebra` is spanned by lists of `CrAnStates`. -/
-abbrev CrAnAlgebra (𝓕 : FieldStruct) : Type := FreeAlgebra ℂ 𝓕.CrAnStates
+abbrev CrAnAlgebra (𝓕 : FieldSpecification) : Type := FreeAlgebra ℂ 𝓕.CrAnStates
 
 namespace CrAnAlgebra
 
@@ -263,4 +263,4 @@ noncomputable def smulLinearMap (c : ℂ) : CrAnAlgebra 𝓕 →ₗ[ℂ] CrAnAlg
 
 end CrAnAlgebra
 
-end FieldStruct
+end FieldSpecification

HepLean/PerturbationTheory/Algebras/CrAnAlgebra/NormalOrder.lean

@@ -3,23 +3,18 @@ Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Tooby-Smith
 -/
-import HepLean.PerturbationTheory.FieldStruct.NormalOrder
+import HepLean.PerturbationTheory.FieldSpecification.NormalOrder
 import HepLean.PerturbationTheory.Algebras.CrAnAlgebra.SuperCommute
 import HepLean.PerturbationTheory.Koszul.KoszulSign
 /-!
 
-# Normal Ordering
+# Normal Ordering in the CrAnAlgebra
 
-The normal ordering puts all creation operators to the left and all annihilation operators to the
-right. It acts on `CrAnStates` and defines a linear map from the `CrAnAlgebra` to itself.
-
-The normal ordering satisfies a number of nice properties with relation to the operator
-algebra 𝓞.A.
 
 -/
 
-namespace FieldStruct
-variable {𝓕 : FieldStruct}
+namespace FieldSpecification
+variable {𝓕 : FieldSpecification}
 open FieldStatistic
 /-!
 
@@ -552,4 +547,4 @@ end
 
 end CrAnAlgebra
 
-end FieldStruct
+end FieldSpecification

HepLean/PerturbationTheory/Algebras/CrAnAlgebra/SuperCommute.lean

@@ -9,8 +9,8 @@ import HepLean.PerturbationTheory.Algebras.CrAnAlgebra.Basic
 # Super Commute
 -/
 
-namespace FieldStruct
-variable {𝓕 : FieldStruct}
+namespace FieldSpecification
+variable {𝓕 : FieldSpecification}
 
 namespace CrAnAlgebra
 
@@ -18,7 +18,7 @@ open StateAlgebra
 
 /-!
 
-## The super commutor on the creation and annihlation algebra.
+## The super commutor on the CrAnAlgebra.
 
 -/
 
@@ -35,7 +35,7 @@ noncomputable def superCommute : 𝓕.CrAnAlgebra →ₗ[ℂ] 𝓕.CrAnAlgebra
 /-- The super commutor on the creation and annihlation algebra. For two bosonic operators
   or a bosonic and fermionic operator this corresponds to the usual commutator
   whilst for two fermionic operators this corresponds to the anti-commutator. -/
-scoped[FieldStruct.CrAnAlgebra] notation "⟨" φs "," φs' "⟩ₛca" => superCommute φs φs'
+scoped[FieldSpecification.CrAnAlgebra] notation "⟨" φs "," φs' "⟩ₛca" => superCommute φs φs'
 
 lemma superCommute_ofCrAnList (φs φs' : List 𝓕.CrAnStates) : ⟨ofCrAnList φs, ofCrAnList φs'⟩ₛca =
     ofCrAnList (φs ++ φs') - 𝓢(𝓕 |>ₛ φs, 𝓕 |>ₛ φs') • ofCrAnList (φs' ++ φs) := by
@@ -421,4 +421,4 @@ lemma superCommute_ofCrAnList_ofStateList_eq_sum (φs : List 𝓕.CrAnStates) :
 
 end CrAnAlgebra
 
-end FieldStruct
+end FieldSpecification