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refactor: Rename States to FieldOps

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jstoobysmith 2025-02-03 11:28:14 +00:00
parent 171e80fc04
commit 8f41de5785
36 changed files with 946 additions and 946 deletions
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22
HepLean/PerturbationTheory/WickContraction/TimeContract.lean
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@ -21,7 +21,7 @@ open FieldOpAlgebra
/-- Given a Wick contraction `φsΛ` associated with a list `φs`, the
product of all time-contractions of pairs of contracted elements in `φs`,
as a member of the center of `𝓞.A`. -/
noncomputable def timeContract {φs : List 𝓕.States}
noncomputable def timeContract {φs : List 𝓕.FieldOp}
(φsΛ : WickContraction φs.length) :
Subalgebra.center ℂ 𝓕.FieldOpAlgebra :=
∏ (a : φsΛ.1), ⟨FieldOpAlgebra.timeContract
@ -35,7 +35,7 @@ This result follows from the fact that `timeContract` only depends on contracted
and `(φsΛ ↩Λ φ i none)` has the 'same' contracted pairs as `φsΛ`. -/
@[simp]
lemma timeContract_insertAndContract_none
(φ : 𝓕.States) (φs : List 𝓕.States)
(φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) :
(φsΛ ↩Λ φ i none).timeContract = φsΛ.timeContract := by
rw [timeContract, insertAndContract_none_prod_contractions]
@ -52,7 +52,7 @@ This follows from the fact that `(φsΛ ↩Λ φ i (some j))` has one more contr
corresponding to `φ` contracted with `φⱼ`. The order depends on whether we insert `φ` before
or after `φⱼ`. -/
lemma timeConract_insertAndContract_some
(φ : 𝓕.States) (φs : List 𝓕.States)
(φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) (j : φsΛ.uncontracted) :
(φsΛ ↩Λ φ i (some j)).timeContract =
(if i < i.succAbove j then
@ -71,7 +71,7 @@ lemma timeConract_insertAndContract_some
simp
@[simp]
lemma timeContract_empty (φs : List 𝓕.States) :
lemma timeContract_empty (φs : List 𝓕.FieldOp) :
(@empty φs.length).timeContract = 1 := by
rw [timeContract, empty]
simp
@ -79,16 +79,16 @@ lemma timeContract_empty (φs : List 𝓕.States) :
open FieldStatistic
lemma timeConract_insertAndContract_some_eq_mul_contractStateAtIndex_lt
(φ : 𝓕.States) (φs : List 𝓕.States)
(φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) (k : φsΛ.uncontracted)
(ht : 𝓕.timeOrderRel φ φs[k.1]) (hik : i < i.succAbove k) :
(φsΛ ↩Λ φ i (some k)).timeContract =
𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ ⟨φs.get, (φsΛ.uncontracted.filter (fun x => x < k))⟩)
• (contractStateAtIndex φ [φsΛ]ᵘᶜ ((uncontractedStatesEquiv φs φsΛ) (some k)) *
• (contractStateAtIndex φ [φsΛ]ᵘᶜ ((uncontractedFieldOpEquiv φs φsΛ) (some k)) *
φsΛ.timeContract) := by
rw [timeConract_insertAndContract_some]
simp only [Nat.succ_eq_add_one, Fin.getElem_fin, ite_mul, instCommGroup.eq_1,
contractStateAtIndex, uncontractedStatesEquiv, Equiv.optionCongr_apply,
contractStateAtIndex, uncontractedFieldOpEquiv, Equiv.optionCongr_apply,
Equiv.coe_trans, Option.map_some', Function.comp_apply, finCongr_apply, Fin.coe_cast,
List.getElem_map, uncontractedList_getElem_uncontractedIndexEquiv_symm, List.get_eq_getElem,
Algebra.smul_mul_assoc, uncontractedListGet]
@ -112,16 +112,16 @@ lemma timeConract_insertAndContract_some_eq_mul_contractStateAtIndex_lt
· exact ht
lemma timeConract_insertAndContract_some_eq_mul_contractStateAtIndex_not_lt
(φ : 𝓕.States) (φs : List 𝓕.States)
(φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) (k : φsΛ.uncontracted)
(ht : ¬ 𝓕.timeOrderRel φs[k.1] φ) (hik : ¬ i < i.succAbove k) :
(φsΛ ↩Λ φ i (some k)).timeContract =
𝓢(𝓕 |>ₛ φ, 𝓕 |>ₛ ⟨φs.get, (φsΛ.uncontracted.filter (fun x => x ≤ k))⟩)
• (contractStateAtIndex φ [φsΛ]ᵘᶜ
((uncontractedStatesEquiv φs φsΛ) (some k)) * φsΛ.timeContract) := by
((uncontractedFieldOpEquiv φs φsΛ) (some k)) * φsΛ.timeContract) := by
rw [timeConract_insertAndContract_some]
simp only [Nat.succ_eq_add_one, Fin.getElem_fin, ite_mul, instCommGroup.eq_1,
contractStateAtIndex, uncontractedStatesEquiv, Equiv.optionCongr_apply,
contractStateAtIndex, uncontractedFieldOpEquiv, Equiv.optionCongr_apply,
Equiv.coe_trans, Option.map_some', Function.comp_apply, finCongr_apply, Fin.coe_cast,
List.getElem_map, uncontractedList_getElem_uncontractedIndexEquiv_symm, List.get_eq_getElem,
Algebra.smul_mul_assoc, uncontractedListGet]
@ -163,7 +163,7 @@ lemma timeConract_insertAndContract_some_eq_mul_contractStateAtIndex_not_lt
simp_all only [Fin.getElem_fin, Nat.succ_eq_add_one, not_lt, false_or]
exact ht
lemma timeContract_of_not_gradingCompliant (φs : List 𝓕.States)
lemma timeContract_of_not_gradingCompliant (φs : List 𝓕.FieldOp)
(φsΛ : WickContraction φs.length) (h : ¬ GradingCompliant φs φsΛ) :
φsΛ.timeContract = 0 := by
rw [timeContract]