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refactor: Docs around Wick's theorem (#289)

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* refactor: Organize supercommute for CrAnAlgebra

* refactor: Normal order results

* refactor: Uncontracted List organization

* refactor: Rename OperatorAlgebra

* refactor: Lint
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Joseph Tooby-Smith 2025-01-22 09:15:13 +00:00 • committed by GitHub
parent 7b396501e7
commit 36d3be1cbf
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HepLean/PerturbationTheory/WicksTheorem.lean
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@ -16,10 +16,10 @@ Wick's theorem is related to Isserlis' theorem in mathematics.
-/
namespace FieldSpecification
variable {𝓕 : FieldSpecification} {𝓞 : 𝓕.OperatorAlgebra}
variable {𝓕 : FieldSpecification} {𝓞 : 𝓕.ProtoOperatorAlgebra}
open CrAnAlgebra
open StateAlgebra
open OperatorAlgebra
open ProtoOperatorAlgebra
open HepLean.List
open WickContraction
open FieldStatistic
@ -192,7 +192,7 @@ lemma sign_timeContract_normalOrder_insertList_some (φ : 𝓕.States) (φs : Li
simp only [Nat.succ_eq_add_one, Fin.getElem_fin, ite_mul, Algebra.smul_mul_assoc,
instCommGroup.eq_1, contractStateAtIndex, uncontractedStatesEquiv, Equiv.optionCongr_apply,
Equiv.coe_trans, Option.map_some', Function.comp_apply, finCongr_apply, Fin.coe_cast,
List.getElem_map, uncontractedList_getElem_uncontractedFinEquiv_symm, List.get_eq_getElem]
List.getElem_map, uncontractedList_getElem_uncontractedIndexEquiv_symm, List.get_eq_getElem]
by_cases h1 : i < i.succAbove ↑k
· simp only [h1, ↓reduceIte, MulMemClass.coe_mul]
rw [timeContract_zero_of_diff_grade]