69 lines
2.1 KiB
Text
69 lines
2.1 KiB
Text
/-
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Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Joseph Tooby-Smith
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-/
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import HepLean.PerturbationTheory.FeynmanDiagrams.Basic
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/-!
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# Feynman diagrams in a complex scalar field theory
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-/
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namespace PhiFour
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open CategoryTheory
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open FeynmanDiagram
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open PreFeynmanRule
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/-- The pre-Feynman rules for a complex scalar theory. -/
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@[simps!]
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def complexScalarFeynmanRules : PreFeynmanRule where
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/- There is 2 types of `half-edge`. -/
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HalfEdgeLabel := Fin 2
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/- There is only 1 type of `edge`. -/
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EdgeLabel := Fin 1
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/- There are two types of `vertex`, two external `0` and internal `1`. -/
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VertexLabel := Fin 3
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edgeLabelMap x :=
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match x with
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| 0 => Over.mk ![0, 1]
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vertexLabelMap x :=
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match x with
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| 0 => Over.mk ![0]
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| 1 => Over.mk ![1]
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| 2 => Over.mk ![0, 0, 1, 1]
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/-- An instance allowing us to use integers for edge labels for complex scalar theory. -/
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instance (a : ℕ) : OfNat complexScalarFeynmanRules.EdgeLabel a where
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ofNat := (a : Fin _)
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/-- An instance allowing us to use integers for half-edge labels for complex scalar theory. -/
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instance (a : ℕ) : OfNat complexScalarFeynmanRules.HalfEdgeLabel a where
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ofNat := (a : Fin _)
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/-- An instance allowing us to use integers for vertex labels for complex scalar theory. -/
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instance (a : ℕ) : OfNat complexScalarFeynmanRules.VertexLabel a where
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ofNat := (a : Fin _)
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/-- The pre feynman rules for complex scalars are finite. -/
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instance : IsFinitePreFeynmanRule complexScalarFeynmanRules where
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edgeLabelDecidable := instDecidableEqFin _
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vertexLabelDecidable := instDecidableEqFin _
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halfEdgeLabelDecidable := instDecidableEqFin _
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vertexMapFintype := fun v =>
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match v with
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| 0 => Fin.fintype _
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| 1 => Fin.fintype _
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| 2 => Fin.fintype _
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edgeMapFintype := fun v =>
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match v with
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| 0 => Fin.fintype _
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vertexMapDecidable := fun v =>
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match v with
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| 0 => instDecidableEqFin _
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| 1 => instDecidableEqFin _
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| 2 => instDecidableEqFin _
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edgeMapDecidable := fun v =>
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match v with
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| 0 => instDecidableEqFin _
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end PhiFour
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