Research proof index

For a list φs = φ₀…φₙ of 𝓕.FieldOp, a Wick contraction φsΛ of φs, an element φ of 𝓕.FieldOp, and a k in φsΛ.uncontracted, (φsΛ ↩Λ φ 0 (some k)).wickTerm is equal to the product of - the sign 𝓢(φ, φ₀…φᵢ₋₁) - the sign φsΛ.sign - φsΛ.staticContract - s • [anPart φ, ofFieldOp φs[k]]ₛ where s is the sign associated with moving `...

For a list φs = φ₀…φₙ of 𝓕.FieldOp, a Wick contraction φsΛ of φs, an element φ of 𝓕.FieldOp, a i ≤ φs.length and a k in φsΛ.uncontracted such that i ≤ k, with the condition that φ has greater or equal time to φs[k], then (φsΛ ↩Λ φ i (some k)).timeContract is equal to the product of - [anPart φ, φs[k]]ₛ - φsΛ.timeContract -...

For a list φs = φ₀…φₙ of 𝓕.FieldOp, a Wick contraction φsΛ of φs, an element φ of 𝓕.FieldOp, a i ≤ φs.length and a k in φsΛ.uncontracted such that k < i, with the condition that φs[k] does not have time greater or equal to φ, then (φsΛ ↩Λ φ i (some k)).timeContract is equal to the product of - [anPart φ, φs[k]]ₛ - `φsΛ.timeCo...

For a list φs = φ₀…φₙ of 𝓕.FieldOp, a Wick contraction φsΛ of φs, an element φ of 𝓕.FieldOp, a i ≤ φs.length and a k in φsΛ.uncontracted, then (φsΛ ↩Λ φ i (some k)).timeContract is equal to the product of - timeContract φ φs[k] if i ≤ k or timeContract φs[k] φ if k < i - φsΛ.timeContract. The proof of this result ultimately...

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...