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doc: Edits to Wick theorem docs

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jstoobysmith 2025-02-10 10:21:57 +00:00
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8
HepLean/PerturbationTheory/WickContraction/Join.lean
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@ -25,7 +25,13 @@ open FieldOpAlgebra
/-- Given a list `φs` of `𝓕.FieldOp`, a Wick contraction `φsΛ` of `φs` and a Wick contraction
`φsucΛ` of `[φsΛ]ᵘᶜ`, `join φsΛ φsucΛ` is defined as the Wick contraction of `φs` consisting of
the contractions in `φsΛ` and those in `φsucΛ`. -/
the contractions in `φsΛ` and those in `φsucΛ`.
As an example, for `φs = [φ1, φ2, φ3, φ4]`,
`φsΛ = {{0, 1}}` corresponding to the contraction of `φ1` and `φ2` in `φs` and
`φsucΛ = {{0, 1}}`
corresponding to the contraction of `φ3` and `φ4` in `[φsΛ]ᵘᶜ = [φ3, φ4]`, then
`join φsΛ φsucΛ` is the contraction `{{0, 1}, {2, 3}}` of `φs`. -/
def join {φs : List 𝓕.FieldOp} (φsΛ : WickContraction φs.length)
(φsucΛ : WickContraction [φsΛ]ᵘᶜ.length) : WickContraction φs.length :=
⟨φsΛ.1 ∪ φsucΛ.1.map (Finset.mapEmbedding uncontractedListEmd).toEmbedding, by