DibyashanuPati/PhysLean
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

feat: More informal details about Wick contract

Browse source
This commit is contained in:
jstoobysmith 2024-12-03 12:55:54 +00:00
parent ec6da248d8
commit 9546e1fdc5
3 changed files with 10 additions and 11 deletions
Download patch file Download diff file Expand all files Collapse all files

13
HepLean/PerturbationTheory/FeynmanDiagrams/Light.lean
View file

@ -3,6 +3,7 @@ Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
import HepLean.PerturbationTheory.Wick.Contract
import HepLean.PerturbationTheory.Wick.Species
/-!
@ -21,8 +22,12 @@ informal_definition FeynmanDiagram where
Let S be a WickSpecies
A Feynman diagram contains the following data:
- A type of vertices 𝓥 → S.𝓯 ⊕ S.𝓘.
- A type of edges 𝓔 → S.𝓕.
- A type of half-edges 𝓱𝓔 → 𝓔 × 𝓥 × S.𝓯.
- A type of edges ed : 𝓔 → S.𝓕.
- A type of half-edges 𝓱𝓔 with maps `e : 𝓱𝓔 → 𝓔`, `v : 𝓱𝓔 → 𝓥` and `f : 𝓱𝓔 → S.𝓯`
Subject to the following conditions:
...
"
- `𝓱𝓔` is a double cover of `𝓔` through `e`. That is,
for each edge `x : 𝓔` there exists an isomorphism between `i : Fin 2 → e⁻¹ 𝓱𝓔 {x}`.
- These isomorphisms must satisfy `⟦f(i(0))⟧ = ⟦f(i(1))⟧ = ed(e)` and `f(i(0)) = S.ξ (f(i(1)))`.
- For each vertex `ver : 𝓥` there exists an isomorphism between the object (roughly)
`(𝓘Fields v).2` and the pullback of `v` along `ver`."
deps :≈ [``Wick.Species]