33 lines
1.4 KiB
Text
33 lines
1.4 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.Wick.Contract
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import HepLean.PerturbationTheory.Wick.Species
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/-!
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# Feynman diagrams
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This file currently contains a lighter implmentation of Feynman digrams than can be found in
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`HepLean.PerturbationTheory.FeynmanDiagrams.Basic`. Eventually this will superseed that file.
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The implmentation here is done in conjunction with Wicks species etc.
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This file is currently a stub.
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-/
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informal_definition FeynmanDiagram where
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math :≈ "
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Let S be a WickSpecies
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A Feynman diagram contains the following data:
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- A type of vertices 𝓥 → S.𝓯 ⊕ S.𝓘.
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- A type of edges ed : 𝓔 → S.𝓕.
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- A type of half-edges 𝓱𝓔 with maps `e : 𝓱𝓔 → 𝓔`, `v : 𝓱𝓔 → 𝓥` and `f : 𝓱𝓔 → S.𝓯`
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Subject to the following conditions:
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- `𝓱𝓔` is a double cover of `𝓔` through `e`. That is,
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for each edge `x : 𝓔` there exists an isomorphism between `i : Fin 2 → e⁻¹ 𝓱𝓔 {x}`.
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- These isomorphisms must satisfy `⟦f(i(0))⟧ = ⟦f(i(1))⟧ = ed(e)` and `f(i(0)) = S.ξ (f(i(1)))`.
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- For each vertex `ver : 𝓥` there exists an isomorphism between the object (roughly)
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`(𝓘Fields v).2` and the pullback of `v` along `ver`."
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deps :≈ [``Wick.Species]
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