2024-06-18 11:40:36 -04:00
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/-
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Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
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Released under Apache 2.0 license.
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Authors: Joseph Tooby-Smith
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-/
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import HepLean.FeynmanDiagrams.Basic
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/-!
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# Feynman diagrams in Phi^4 theory
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The aim of this file is to start building up the theory of Feynman diagrams in the context of
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Phi^4 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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2024-06-18 13:07:49 -04:00
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/-- The pre-Feynman rules for `Phi^4` theory. -/
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2024-06-18 11:40:36 -04:00
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@[simps!]
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def phi4PreFeynmanRules : PreFeynmanRule where
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/- There is only 1 type of `half-edge`. -/
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HalfEdgeLabel := Fin 1
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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`, external `0` and internal `1`. -/
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VertexLabel := Fin 2
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edgeLabelMap x :=
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match x with
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| 0 => Over.mk ![0, 0]
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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 ![0, 0, 0, 0]
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instance (a : ℕ) : OfNat phi4PreFeynmanRules.EdgeLabel a where
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ofNat := (a : Fin _)
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instance (a : ℕ) : OfNat phi4PreFeynmanRules.HalfEdgeLabel a where
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ofNat := (a : Fin _)
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instance (a : ℕ) : OfNat phi4PreFeynmanRules.VertexLabel a where
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ofNat := (a : Fin _)
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instance : IsFinitePreFeynmanRule phi4PreFeynmanRules 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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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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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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