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refactor: Slight adjustments to doc-strings

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jstoobysmith 2025-02-12 06:14:11 +00:00
parent 3fc88eaca8
commit ea29b15e4a
15 changed files with 64 additions and 30 deletions
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6
HepLean/PerturbationTheory/FieldOpAlgebra/WicksTheoremNormal.lean
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@ -23,7 +23,7 @@ open EqTimeOnly
/--
For a list `φs` of `𝓕.FieldOp`, then
`𝓣(φs) = ∑ φsΛ, φsΛ.1.wickTerm • φsΛ.1.timeContract.1 * 𝓣(𝓝(ofFieldOpList [φsΛ.1]ᵘᶜ))`
`𝓣(φs) = ∑ φsΛ, φsΛ.sign • φsΛ.timeContract * 𝓣(𝓝([φsΛ]ᵘᶜ))`
where the sum is over all Wick contraction `φsΛ` which only have equal time contractions.
@ -92,7 +92,7 @@ lemma timeOrder_ofFieldOpList_eq_eqTimeOnly_empty (φs : List 𝓕.FieldOp) :
/--
For a list `φs` of `𝓕.FieldOp`, then
`𝓣(𝓝(φs)) = 𝓣(φs) - ∑ φsΛ, φsΛ.1.wickTerm • φsΛ.1.timeContract.1 * 𝓣(𝓝(ofFieldOpList [φsΛ.1]ᵘᶜ))`
`𝓣(𝓝(φs)) = 𝓣(φs) - ∑ φsΛ, φsΛ.sign • φsΛ.timeContract.1 * 𝓣(𝓝([φsΛ]ᵘᶜ))`
where the sum is over all *non-empty* Wick contraction `φsΛ` which only
have equal time contractions.
@ -222,7 +222,7 @@ lemma wicks_theorem_normal_order_empty : 𝓣(𝓝(ofFieldOpList [])) =
where the sum is over all Wick contraction `φsΛ` in which no two contracted elements
have the same time.
The proof of proceeds by induction on `φs`, with the base case `[]` holding by following
The proof proceeds by induction on `φs`, with the base case `[]` holding by following
through definitions. and the inductive case holding as a result of
- `timeOrder_haveEqTime_split`
- `normalOrder_timeOrder_ofFieldOpList_eq_eqTimeOnly_empty`