Research proof index

The embedding of Fin [φsΛ]ᵘᶜ.length into Fin φs.length. -/ def uncontractedListEmd {φs : List 𝓕.FieldOp} {φsΛ : WickContraction φs.length} : Fin [φsΛ]ᵘᶜ.length ↪ Fin φs.length := ((finCongr (by simp [uncontractedListGet])).trans φsΛ.uncontractedIndexEquiv).toEmbedding.trans (Function.Embedding.subtype fun x => x ∈ φsΛ.uncontracted) lemma uncontracted...

For a list φs = φ₀…φₙ of 𝓕.FieldOp, a Wick contraction φsΛ of φs, an element φ of 𝓕.FieldOp, and i ≤ φs.length, then (φsΛ ↩Λ φ i none).wickTerm is equal to 𝓢(φ, φ₀…φᵢ₋₁) φsΛ.sign • φsΛ.timeContract * 𝓝(φ :: [φsΛ]ᵘᶜ) The proof of this result relies on - normalOrder_uncontracted_none to rewrite normal orderings. - `timeContract_inser...

For a list φs = φ₀…φₙ of 𝓕.FieldOp, a Wick contraction φsΛ of φs, an element φ of 𝓕.FieldOp, i ≤ φs.length and a k in φsΛ.uncontracted, such that all 𝓕.FieldOp in φ₀…φᵢ₋₁ have time strictly less than φ and φ has a time greater than or equal to all FieldOp in φ₀…φₙ, then (φsΛ ↩Λ φ i (some k)).staticWickTerm is equal to th...