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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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48
HepLean/PerturbationTheory/WickContraction/InsertAndContract.lean
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@ -29,7 +29,7 @@ open HepLean.Fin
`j : Option (c.uncontracted)` of `c`.
The Wick contraction associated with `(φs.insertIdx i φ).length` formed by 'inserting' `φ`
into `φs` after the first `i` elements and contracting it optionally with j. -/
def insertAndContract {φs : List 𝓕.States} (φ : 𝓕.States) (φsΛ : WickContraction φs.length)
def insertAndContract {φs : List 𝓕.FieldOp} (φ : 𝓕.FieldOp) (φsΛ : WickContraction φs.length)
(i : Fin φs.length.succ) (j : Option φsΛ.uncontracted) :
WickContraction (φs.insertIdx i φ).length :=
congr (by simp) (φsΛ.insertAndContractNat i j)
@ -38,7 +38,7 @@ def insertAndContract {φs : List 𝓕.States} (φ : 𝓕.States) (φsΛ : WickC
scoped[WickContraction] notation φs "↩Λ" φ:max i:max j => insertAndContract φ φs i j
@[simp]
lemma insertAndContract_fstFieldOfContract (φ : 𝓕.States) (φs : List 𝓕.States)
lemma insertAndContract_fstFieldOfContract (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) (j : Option φsΛ.uncontracted)
(a : φsΛ.1) : (φsΛ ↩Λ φ i j).fstFieldOfContract
(congrLift (insertIdx_length_fin φ φs i).symm (insertLift i j a)) =
@ -46,7 +46,7 @@ lemma insertAndContract_fstFieldOfContract (φ : 𝓕.States) (φs : List 𝓕.S
simp [insertAndContract]
@[simp]
lemma insertAndContract_sndFieldOfContract (φ : 𝓕.States) (φs : List 𝓕.States)
lemma insertAndContract_sndFieldOfContract (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) (j : Option (φsΛ.uncontracted))
(a : φsΛ.1) : (φsΛ ↩Λ φ i j).sndFieldOfContract
(congrLift (insertIdx_length_fin φ φs i).symm (insertLift i j a)) =
@ -54,7 +54,7 @@ lemma insertAndContract_sndFieldOfContract (φ : 𝓕.States) (φs : List 𝓕.S
simp [insertAndContract]
@[simp]
lemma insertAndContract_fstFieldOfContract_some_incl (φ : 𝓕.States) (φs : List 𝓕.States)
lemma insertAndContract_fstFieldOfContract_some_incl (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) (j : φsΛ.uncontracted) :
(insertAndContract φ φsΛ i (some j)).fstFieldOfContract
(congrLift (insertIdx_length_fin φ φs i).symm ⟨{i, i.succAbove j}, by
@ -92,7 +92,7 @@ lemma insertAndContract_fstFieldOfContract_some_incl (φ : 𝓕.States) (φs : L
-/
@[simp]
lemma insertAndContract_none_getDual?_self (φ : 𝓕.States) (φs : List 𝓕.States)
lemma insertAndContract_none_getDual?_self (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) :
(φsΛ ↩Λ φ i none).getDual? (Fin.cast (insertIdx_length_fin φ φs i).symm i) = none := by
simp only [Nat.succ_eq_add_one, insertAndContract, getDual?_congr, finCongr_apply, Fin.cast_trans,
@ -100,27 +100,27 @@ lemma insertAndContract_none_getDual?_self (φ : 𝓕.States) (φs : List 𝓕.S
have h1 := φsΛ.insertAndContractNat_none_getDual?_isNone i
simpa using h1
lemma insertAndContract_isSome_getDual?_self (φ : 𝓕.States) (φs : List 𝓕.States)
lemma insertAndContract_isSome_getDual?_self (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)).getDual?
(Fin.cast (insertIdx_length_fin φ φs i).symm i)).isSome := by
simp [insertAndContract, getDual?_congr]
lemma insertAndContract_some_getDual?_self_not_none (φ : 𝓕.States) (φs : List 𝓕.States)
lemma insertAndContract_some_getDual?_self_not_none (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)).getDual?
(Fin.cast (insertIdx_length_fin φ φs i).symm i)) = none := by
simp [insertAndContract, getDual?_congr]
@[simp]
lemma insertAndContract_some_getDual?_self_eq (φ : 𝓕.States) (φs : List 𝓕.States)
lemma insertAndContract_some_getDual?_self_eq (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)).getDual? (Fin.cast (insertIdx_length_fin φ φs i).symm i))
= some (Fin.cast (insertIdx_length_fin φ φs i).symm (i.succAbove j)) := by
simp [insertAndContract, getDual?_congr]
@[simp]
lemma insertAndContract_some_getDual?_some_eq (φ : 𝓕.States) (φs : List 𝓕.States)
lemma insertAndContract_some_getDual?_some_eq (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)).getDual?
(Fin.cast (insertIdx_length_fin φ φs i).symm (i.succAbove j)))
@ -131,14 +131,14 @@ lemma insertAndContract_some_getDual?_some_eq (φ : 𝓕.States) (φs : List
simp
@[simp]
lemma insertAndContract_none_succAbove_getDual?_eq_none_iff (φ : 𝓕.States) (φs : List 𝓕.States)
lemma insertAndContract_none_succAbove_getDual?_eq_none_iff (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) (j : Fin φs.length) :
(φsΛ ↩Λ φ i none).getDual? (Fin.cast (insertIdx_length_fin φ φs i).symm
(i.succAbove j)) = none ↔ φsΛ.getDual? j = none := by
simp [insertAndContract, getDual?_congr]
@[simp]
lemma insertAndContract_some_succAbove_getDual?_eq_option (φ : 𝓕.States) (φs : List 𝓕.States)
lemma insertAndContract_some_succAbove_getDual?_eq_option (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) (j : Fin φs.length)
(k : φsΛ.uncontracted) (hkj : j ≠ k.1) :
(φsΛ ↩Λ φ i (some k)).getDual? (Fin.cast (insertIdx_length_fin φ φs i).symm
@ -150,7 +150,7 @@ lemma insertAndContract_some_succAbove_getDual?_eq_option (φ : 𝓕.States) (φ
rfl
@[simp]
lemma insertAndContract_none_succAbove_getDual?_isSome_iff (φ : 𝓕.States) (φs : List 𝓕.States)
lemma insertAndContract_none_succAbove_getDual?_isSome_iff (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) (j : Fin φs.length) :
((φsΛ ↩Λ φ i none).getDual? (Fin.cast (insertIdx_length_fin φ φs i).symm
(i.succAbove j))).isSome ↔ (φsΛ.getDual? j).isSome := by
@ -158,7 +158,7 @@ lemma insertAndContract_none_succAbove_getDual?_isSome_iff (φ : 𝓕.States) (
simp
@[simp]
lemma insertAndContract_none_getDual?_get_eq (φ : 𝓕.States) (φs : List 𝓕.States)
lemma insertAndContract_none_getDual?_get_eq (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) (j : Fin φs.length)
(h : ((φsΛ ↩Λ φ i none).getDual? (Fin.cast (insertIdx_length_fin φ φs i).symm
(i.succAbove j))).isSome) :
@ -169,7 +169,7 @@ lemma insertAndContract_none_getDual?_get_eq (φ : 𝓕.States) (φs : List 𝓕
/-........................................... -/
@[simp]
lemma insertAndContract_sndFieldOfContract_some_incl (φ : 𝓕.States) (φs : List 𝓕.States)
lemma insertAndContract_sndFieldOfContract_some_incl (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)).sndFieldOfContract
(congrLift (insertIdx_length_fin φ φs i).symm ⟨{i, i.succAbove j}, by
@ -201,7 +201,7 @@ lemma insertAndContract_sndFieldOfContract_some_incl (φ : 𝓕.States) (φs : L
have hi : i.succAbove j ≠ i := Fin.succAbove_ne i j
omega
lemma insertAndContract_none_prod_contractions (φ : 𝓕.States) (φs : List 𝓕.States)
lemma insertAndContract_none_prod_contractions (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ)
(f : (φsΛ ↩Λ φ i none).1 → M) [CommMonoid M] :
∏ a, f a = ∏ (a : φsΛ.1), f (congrLift (insertIdx_length_fin φ φs i).symm
@ -213,7 +213,7 @@ lemma insertAndContract_none_prod_contractions (φ : 𝓕.States) (φs : List
erw [← e1.prod_comp]
rfl
lemma insertAndContract_some_prod_contractions (φ : 𝓕.States) (φs : List 𝓕.States)
lemma insertAndContract_some_prod_contractions (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
(φsΛ : WickContraction φs.length) (i : Fin φs.length.succ) (j : φsΛ.uncontracted)
(f : (φsΛ ↩Λ φ i (some j)).1 → M) [CommMonoid M] :
∏ a, f a = f (congrLift (insertIdx_length_fin φ φs i).symm
@ -231,13 +231,13 @@ lemma insertAndContract_some_prod_contractions (φ : 𝓕.States) (φs : List
/-- Given a finite set of `Fin φs.length` the finite set of `(φs.insertIdx i φ).length`
formed by mapping elements using `i.succAboveEmb` and `finCongr`. -/
def insertAndContractLiftFinset (φ : 𝓕.States) {φs : List 𝓕.States}
def insertAndContractLiftFinset (φ : 𝓕.FieldOp) {φs : List 𝓕.FieldOp}
(i : Fin φs.length.succ) (a : Finset (Fin φs.length)) :
Finset (Fin (φs.insertIdx i φ).length) :=
(a.map i.succAboveEmb).map (finCongr (insertIdx_length_fin φ φs i).symm).toEmbedding
@[simp]
lemma self_not_mem_insertAndContractLiftFinset (φ : 𝓕.States) {φs : List 𝓕.States}
lemma self_not_mem_insertAndContractLiftFinset (φ : 𝓕.FieldOp) {φs : List 𝓕.FieldOp}
(i : Fin φs.length.succ) (a : Finset (Fin φs.length)) :
Fin.cast (insertIdx_length_fin φ φs i).symm i ∉ insertAndContractLiftFinset φ i a := by
simp only [Nat.succ_eq_add_one, insertAndContractLiftFinset, Finset.mem_map_equiv, finCongr_symm,
@ -246,7 +246,7 @@ lemma self_not_mem_insertAndContractLiftFinset (φ : 𝓕.States) {φs : List
intro x
exact fun a => Fin.succAbove_ne i x
lemma succAbove_mem_insertAndContractLiftFinset (φ : 𝓕.States) {φs : List 𝓕.States}
lemma succAbove_mem_insertAndContractLiftFinset (φ : 𝓕.FieldOp) {φs : List 𝓕.FieldOp}
(i : Fin φs.length.succ) (a : Finset (Fin φs.length)) (j : Fin φs.length) :
Fin.cast (insertIdx_length_fin φ φs i).symm (i.succAbove j)
∈ insertAndContractLiftFinset φ i a ↔ j ∈ a := by
@ -261,7 +261,7 @@ lemma succAbove_mem_insertAndContractLiftFinset (φ : 𝓕.States) {φs : List
· intro h
use j
lemma insert_fin_eq_self (φ : 𝓕.States) {φs : List 𝓕.States}
lemma insert_fin_eq_self (φ : 𝓕.FieldOp) {φs : List 𝓕.FieldOp}
(i : Fin φs.length.succ) (j : Fin (List.insertIdx i φ φs).length) :
j = Fin.cast (insertIdx_length_fin φ φs i).symm i
∨ ∃ k, j = Fin.cast (insertIdx_length_fin φ φs i).symm (i.succAbove k) := by
@ -276,7 +276,7 @@ lemma insert_fin_eq_self (φ : 𝓕.States) {φs : List 𝓕.States}
use z
rfl
lemma insertLift_sum (φ : 𝓕.States) {φs : List 𝓕.States}
lemma insertLift_sum (φ : 𝓕.FieldOp) {φs : List 𝓕.FieldOp}
(i : Fin φs.length.succ) [AddCommMonoid M] (f : WickContraction (φs.insertIdx i φ).length → M) :
∑ c, f c =
∑ (φsΛ : WickContraction φs.length), ∑ (k : Option φsΛ.uncontracted), f (φsΛ ↩Λ φ i k) := by
@ -289,7 +289,7 @@ lemma insertLift_sum (φ : 𝓕.States) {φs : List 𝓕.States}
## Uncontracted list
-/
lemma insertAndContract_uncontractedList_none_map (φ : 𝓕.States) {φs : List 𝓕.States}
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.uncontractedListOrderPos i) φ [φsΛ]ᵘᶜ := by
simp only [Nat.succ_eq_add_one, insertAndContract, uncontractedListGet]
@ -305,14 +305,14 @@ lemma insertAndContract_uncontractedList_none_map (φ : 𝓕.States) {φs : List
rfl
@[simp]
lemma insertAndContract_uncontractedList_none_zero (φ : 𝓕.States) {φs : List 𝓕.States}
lemma insertAndContract_uncontractedList_none_zero (φ : 𝓕.FieldOp) {φs : List 𝓕.FieldOp}
(φsΛ : WickContraction φs.length) :
[φsΛ ↩Λ φ 0 none]ᵘᶜ = φ :: [φsΛ]ᵘᶜ := by
rw [insertAndContract_uncontractedList_none_map]
simp [uncontractedListOrderPos]
open FieldStatistic in
lemma stat_ofFinset_of_insertAndContractLiftFinset (φ : 𝓕.States) (φs : List 𝓕.States)
lemma stat_ofFinset_of_insertAndContractLiftFinset (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp)
(i : Fin φs.length.succ) (a : Finset (Fin φs.length)) :
(𝓕 |>ₛ ⟨(φs.insertIdx i φ).get, insertAndContractLiftFinset φ i a⟩) = 𝓕 |>ₛ ⟨φs.get, a⟩ := by
simp only [ofFinset, Nat.succ_eq_add_one]