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/StateAlgebra/Basic.lean

@@ -3,7 +3,7 @@ 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.CreateAnnihilate
+import HepLean.PerturbationTheory.FieldSpecification.CreateAnnihilate
 /-!
 
 # State algebra
@@ -13,14 +13,14 @@ generated by the states.
 
 -/
 
-namespace FieldStruct
-variable {𝓕 : FieldStruct}
+namespace FieldSpecification
+variable {𝓕 : FieldSpecification}
 
 /-- The state free-algebra.
   The free algebra generated by `States`,
   that is a position based states or assymptotic states.
   As a module `StateAlgebra` is spanned by lists of `States`. -/
-abbrev StateAlgebra (𝓕 : FieldStruct) : Type := FreeAlgebra ℂ 𝓕.States
+abbrev StateAlgebra (𝓕 : FieldSpecification) : Type := FreeAlgebra ℂ 𝓕.States
 
 namespace StateAlgebra
 
@@ -90,4 +90,4 @@ lemma superCommute_ofList (φs φs' : List 𝓕.States) : ⟨ofList φs, ofList
 
 end StateAlgebra
 
-end FieldStruct
+end FieldSpecification

HepLean/PerturbationTheory/Algebras/StateAlgebra/TimeOrder.lean

@@ -3,19 +3,16 @@ 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.TimeOrder
+import HepLean.PerturbationTheory.FieldSpecification.TimeOrder
 import HepLean.PerturbationTheory.Koszul.KoszulSign
 /-!
 
-# State algebra
-
-We define the state algebra of a field structure to be the free algebra
-generated by the states.
+# Time ordering on the state algebra
 
 -/
 
-namespace FieldStruct
-variable {𝓕 : FieldStruct}
+namespace FieldSpecification
+variable {𝓕 : FieldSpecification}
 noncomputable section
 
 namespace StateAlgebra
@@ -80,4 +77,4 @@ lemma timeOrder_eq_maxTimeField_mul (φ : 𝓕.States) (φs : List 𝓕.States)
 
 end StateAlgebra
 end
-end FieldStruct
+end FieldSpecification