Insert And Contract uncontracted List none map
WickContraction.insertAndContract_uncontractedList_none_map
Plain-language statement
For a list φs of 𝓕.FieldOp, a Wick contraction φsΛ of φs, an element φ of 𝓕.FieldOp and a i ≤ φs.length then a sum over Wick contractions of φs with φ inserted at i is equal to the sum over Wick contractions φsΛ of just φs and the sum over optional uncontracted elements of the φsΛ. In other words, `∑ (φsΛ : WickContraction (φs....
Exact Lean statement
lemma insertAndContract_uncontractedList_none_map (φ : 𝓕.FieldOp) {φs : List 𝓕.FieldOp}
(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) :
[φsΛ ↩Λ φ i none]ᵘᶜ = List.insertIdx [φsΛ]ᵘᶜ (φsΛ.uncontractedListOrderPos i) φFormal artifact
Lean source
lemma insertAndContract_uncontractedList_none_map (φ : 𝓕.FieldOp) {φs : List 𝓕.FieldOp} (φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) : [φsΛ ↩Λ φ i none]ᵘᶜ = List.insertIdx [φsΛ]ᵘᶜ (φsΛ.uncontractedListOrderPos i) φ := by simp only [Nat.succ_eq_add_one, insertAndContract, uncontractedListGet] rw [congr_uncontractedList] erw [uncontractedList_extractEquiv_symm_none] rw [orderedInsert_succAboveEmb_uncontractedList_eq_insertIdx] rw [insertIdx_map, insertIdx_map] congr 1 · simp · simp- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/QFT/PerturbationTheory/WickContraction/InsertAndContract.lean:321-331
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