feat: Generalise Feynman diagrams

HepLean/FeynmanDiagrams/Instances/Phi4.lean

@@ -0,0 +1,83 @@
+/-
+Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
+Released under Apache 2.0 license.
+Authors: Joseph Tooby-Smith
+-/
+import HepLean.FeynmanDiagrams.Basic
+/-!
+# Feynman diagrams in Phi^4 theory
+
+The aim of this file is to start building up the theory of Feynman diagrams in the context of
+Phi^4 theory.
+
+
+-/
+
+
+namespace PhiFour
+open CategoryTheory
+open FeynmanDiagram
+open PreFeynmanRule
+
+@[simps!]
+def phi4PreFeynmanRules : PreFeynmanRule where
+  /- There is only 1 type of `half-edge`. -/
+  HalfEdgeLabel := Fin 1
+  /- There is only 1 type of `edge`. -/
+  EdgeLabel := Fin 1
+  /- There are two types of `vertex`, external `0` and internal `1`. -/
+  VertexLabel := Fin 2
+  edgeLabelMap x :=
+    match x with
+    | 0 => Over.mk ![0, 0]
+  vertexLabelMap x :=
+    match x with
+    | 0 => Over.mk ![0]
+    | 1 => Over.mk ![0, 0, 0, 0]
+
+instance (a : ℕ) : OfNat phi4PreFeynmanRules.EdgeLabel a where
+  ofNat := (a : Fin _)
+
+instance (a : ℕ) : OfNat phi4PreFeynmanRules.HalfEdgeLabel a where
+  ofNat := (a : Fin _)
+
+instance (a : ℕ) : OfNat phi4PreFeynmanRules.VertexLabel a where
+  ofNat := (a : Fin _)
+
+
+instance : IsFinitePreFeynmanRule phi4PreFeynmanRules where
+  edgeLabelDecidable :=  instDecidableEqFin _
+  vertexLabelDecidable := instDecidableEqFin _
+  halfEdgeLabelDecidable := instDecidableEqFin _
+  vertexMapFintype := fun v =>
+    match v with
+    | 0 => Fin.fintype _
+    | 1  => Fin.fintype _
+  edgeMapFintype := fun v =>
+    match v with
+    | 0 => Fin.fintype _
+  vertexMapDecidable := fun v =>
+    match v with
+    | 0 => instDecidableEqFin _
+    | 1  => instDecidableEqFin _
+  edgeMapDecidable := fun v =>
+    match v with
+    | 0 => instDecidableEqFin _
+
+
+def figureEight : FeynmanDiagram phi4PreFeynmanRules :=
+  mk' ![0, 0] ![1] ![⟨0, 0, 0⟩, ⟨0, 0, 0⟩, ⟨0, 1, 0⟩, ⟨0, 1, 0⟩] (by decide)
+
+instance : IsFiniteDiagram figureEight where
+  𝓔Fintype := Fin.fintype _
+  𝓔DecidableEq := instDecidableEqFin _
+  𝓥Fintype := Fin.fintype _
+  𝓥DecidableEq := instDecidableEqFin _
+  𝓱𝓔Fintype := Fin.fintype _
+  𝓱𝓔DecidableEq := instDecidableEqFin _
+
+#eval symmetryFactor figureEight
+
+#eval Connected figureEight
+
+end PhiFour