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docs: More doc strings

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jstoobysmith 2024-11-12 05:49:43 +00:00
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10
HepLean/FeynmanDiagrams/Momentum.lean
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@ -48,8 +48,10 @@ We define the direct sum of the edge and vertex momentum spaces.
Corresponding to that spanned by its momentum. -/
def HalfEdgeMomenta : Type := F.𝓱𝓔 → ℝ
/-- The half momenta carries the structure of an addative commutative group. -/
instance : AddCommGroup F.HalfEdgeMomenta := Pi.addCommGroup
/-- The half momenta carries the structure of a module over `ℝ`. Defined via its target. -/
instance : Module ℝ F.HalfEdgeMomenta := Pi.module _ _ _
/-- An auxiliary function used to define the Euclidean inner product on `F.HalfEdgeMomenta`. -/
@ -81,16 +83,20 @@ def euclidInner : F.HalfEdgeMomenta →ₗ[ℝ] F.HalfEdgeMomenta →ₗ[ℝ]
Corresponding to that spanned by its total outflowing momentum. -/
def EdgeMomenta : Type := F.𝓔 → ℝ
/-- The edge momenta form an addative commuative group. -/
instance : AddCommGroup F.EdgeMomenta := Pi.addCommGroup
/-- The edge momenta form a module over `ℝ`. -/
instance : Module ℝ F.EdgeMomenta := Pi.module _ _ _
/-- The type which assocaites to each ege a `1`-dimensional vector space.
Corresponding to that spanned by its total inflowing momentum. -/
def VertexMomenta : Type := F.𝓥 → ℝ
/-- The vertex momenta carries the structure of an addative commuative group. -/
instance : AddCommGroup F.VertexMomenta := Pi.addCommGroup
/-- The vertex momenta carries the structure of a module over `ℝ`. -/
instance : Module ℝ F.VertexMomenta := Pi.module _ _ _
/-- The map from `Fin 2` to `Type` landing on `EdgeMomenta` and `VertexMomenta`. -/
@ -99,11 +105,15 @@ def EdgeVertexMomentaMap : Fin 2 → Type := fun i =>
| 0 => F.EdgeMomenta
| 1 => F.VertexMomenta
/-- The target of the map `EdgeVertexMomentaMap` is either the type of edge momenta
or vertex momenta and thus carries the structure of an addative commuative group. -/
instance (i : Fin 2) : AddCommGroup (EdgeVertexMomentaMap F i) :=
match i with
| 0 => instAddCommGroupEdgeMomenta F
| 1 => instAddCommGroupVertexMomenta F
/-- The target of the map `EdgeVertexMomentaMap` is either the type of edge momenta
or vertex momenta and thus carries the structure of a module over `ℝ`. -/
instance (i : Fin 2) : Module ℝ (EdgeVertexMomentaMap F i) :=
match i with
| 0 => instModuleRealEdgeMomenta F