diff --git a/HepLean/PerturbationTheory/Algebras/CrAnAlgebra/NormalOrder.lean b/HepLean/PerturbationTheory/Algebras/CrAnAlgebra/NormalOrder.lean index 07f3e12..d5a99b0 100644 --- a/HepLean/PerturbationTheory/Algebras/CrAnAlgebra/NormalOrder.lean +++ b/HepLean/PerturbationTheory/Algebras/CrAnAlgebra/NormalOrder.lean @@ -175,7 +175,7 @@ lemma normalOrder_swap_create_annihlate_ofCrAnList (Ο†c Ο†a : 𝓕.CrAnStates) rfl lemma normalOrder_swap_create_annihlate (Ο†c Ο†a : 𝓕.CrAnStates) - (hΟ†c : 𝓕 |>ᢜ Ο†c = CreateAnnihilate.create) (hΟ†a : 𝓕 |>ᢜ Ο†a = CreateAnnihilate.annihilate) + (hΟ†c : 𝓕 |>ᢜ Ο†c = CreateAnnihilate.create) (hΟ†a : 𝓕 |>ᢜ Ο†a = CreateAnnihilate.annihilate) (a b : 𝓕.CrAnAlgebra) : normalOrder (a * ofCrAnState Ο†c * ofCrAnState Ο†a * b) = 𝓒(𝓕 |>β‚› Ο†c, 𝓕 |>β‚› Ο†a) β€’ @@ -258,7 +258,6 @@ Using the results from above. -/ - lemma normalOrder_swap_anPart_crPart (Ο† Ο†' : 𝓕.States) (a b : CrAnAlgebra 𝓕) : normalOrder (a * (anPart (StateAlgebra.ofState Ο†)) * (crPart (StateAlgebra.ofState Ο†')) * b) = 𝓒(𝓕 |>β‚› Ο†, 𝓕 |>β‚› Ο†') β€’ normalOrder (a * (crPart (StateAlgebra.ofState Ο†')) * diff --git a/HepLean/PerturbationTheory/Algebras/CrAnAlgebra/SuperCommute.lean b/HepLean/PerturbationTheory/Algebras/CrAnAlgebra/SuperCommute.lean index 47b89f9..a2f2757 100644 --- a/HepLean/PerturbationTheory/Algebras/CrAnAlgebra/SuperCommute.lean +++ b/HepLean/PerturbationTheory/Algebras/CrAnAlgebra/SuperCommute.lean @@ -209,7 +209,6 @@ lemma superCommute_anPart_anPart (Ο† Ο†' : 𝓕.States) : rw [← ofCrAnList_singleton, ← ofCrAnList_singleton, superCommute_ofCrAnList_ofCrAnList] simp [crAnStatistics, ← ofCrAnList_append] - lemma superCommute_crPart_ofStateList (Ο† : 𝓕.States) (Ο†s : List 𝓕.States) : ⟨crPart (StateAlgebra.ofState Ο†), ofStateList Ο†sβŸ©β‚›ca = crPart (StateAlgebra.ofState Ο†) * ofStateList Ο†s - 𝓒(𝓕 |>β‚› Ο†, 𝓕 |>β‚› Ο†s) β€’ ofStateList Ο†s * @@ -294,7 +293,6 @@ lemma ofStateList_mul_ofState_eq_superCommute (Ο†s : List 𝓕.States) (Ο† : rw [superCommute_ofStateList_ofState] simp - lemma crPart_mul_anPart_eq_superCommute (Ο† Ο†' : 𝓕.States) : crPart (StateAlgebra.ofState Ο†) * anPart (StateAlgebra.ofState Ο†') = 𝓒(𝓕 |>β‚› Ο†, 𝓕 |>β‚› Ο†') β€’ anPart (StateAlgebra.ofState Ο†') * crPart (StateAlgebra.ofState Ο†) + @@ -406,7 +404,6 @@ lemma superCommute_ofCrAnList_ofStateList_cons (Ο† : 𝓕.States) (Ο†s : List rw [ofStateList_cons, mul_assoc, smul_smul, FieldStatistic.ofList_cons_eq_mul] simp [mul_comm] - lemma superCommute_ofCrAnList_ofCrAnList_eq_sum (Ο†s : List 𝓕.CrAnStates) : (Ο†s' : List 𝓕.CrAnStates) β†’ ⟨ofCrAnList Ο†s, ofCrAnList Ο†s'βŸ©β‚›ca = diff --git a/HepLean/PerturbationTheory/FieldSpecification/Examples.lean b/HepLean/PerturbationTheory/FieldSpecification/Examples.lean index dfb714c..c93cbbb 100644 --- a/HepLean/PerturbationTheory/FieldSpecification/Examples.lean +++ b/HepLean/PerturbationTheory/FieldSpecification/Examples.lean @@ -8,7 +8,6 @@ import HepLean.PerturbationTheory.FieldSpecification.Basic # Specific examples of field specifications - -/ namespace FieldSpecification diff --git a/HepLean/PerturbationTheory/FieldSpecification/NormalOrder.lean b/HepLean/PerturbationTheory/FieldSpecification/NormalOrder.lean index c7bfac4..9bdacdf 100644 --- a/HepLean/PerturbationTheory/FieldSpecification/NormalOrder.lean +++ b/HepLean/PerturbationTheory/FieldSpecification/NormalOrder.lean @@ -10,8 +10,6 @@ import HepLean.PerturbationTheory.FieldSpecification.Filters # Normal Ordering of states - - -/ namespace FieldSpecification diff --git a/HepLean/PerturbationTheory/WickContraction/Sign.lean b/HepLean/PerturbationTheory/WickContraction/Sign.lean index 7804cfc..2c1091a 100644 --- a/HepLean/PerturbationTheory/WickContraction/Sign.lean +++ b/HepLean/PerturbationTheory/WickContraction/Sign.lean @@ -903,7 +903,7 @@ lemma stat_signFinset_insert_some_self_snd (Ο† : 𝓕.States) (Ο†s : List 𝓕.S lemma signInsertSomeCoef_eq_finset (Ο† : 𝓕.States) (Ο†s : List 𝓕.States) (c : WickContraction Ο†s.length) (i : Fin Ο†s.length.succ) (j : c.uncontracted) - (hΟ†j : (𝓕 |>β‚› Ο†) = (𝓕 |>β‚› Ο†s[j.1])) : c.signInsertSomeCoef Ο† Ο†s i j = + (hΟ†j : (𝓕 |>β‚› Ο†) = (𝓕 |>β‚› Ο†s[j.1])) : c.signInsertSomeCoef Ο† Ο†s i j = if i < i.succAbove j then 𝓒(𝓕 |>β‚› Ο†, 𝓕 |>β‚› βŸ¨Ο†s.get, (Finset.univ.filter (fun x => i < i.succAbove x ∧ x < j ∧ ((c.getDual? x = none) ∨ diff --git a/HepLean/PerturbationTheory/WickContraction/TimeContract.lean b/HepLean/PerturbationTheory/WickContraction/TimeContract.lean index 260eeb3..362045a 100644 --- a/HepLean/PerturbationTheory/WickContraction/TimeContract.lean +++ b/HepLean/PerturbationTheory/WickContraction/TimeContract.lean @@ -18,12 +18,6 @@ namespace WickContraction variable {n : β„•} (c : WickContraction n) open HepLean.List -/-! - -## Time contract. - --/ - /-- Given a Wick contraction `c` associated with a list `Ο†s`, the product of all time-contractions of pairs of contracted elements in `Ο†s`, as a member of the center of `π“ž.A`. -/ diff --git a/HepLean/PerturbationTheory/WickContraction/UncontractedList.lean b/HepLean/PerturbationTheory/WickContraction/UncontractedList.lean index fafc8c3..e3aed04 100644 --- a/HepLean/PerturbationTheory/WickContraction/UncontractedList.lean +++ b/HepLean/PerturbationTheory/WickContraction/UncontractedList.lean @@ -219,7 +219,6 @@ lemma uncontractedList_length_eq_card (c : WickContraction n) : rw [uncontractedList_eq_sort] exact Finset.length_sort fun x1 x2 => x1 ≀ x2 - lemma filter_uncontractedList (c : WickContraction n) (p : Fin n β†’ Prop) [DecidablePred p] : (c.uncontractedList.filter p) = (c.uncontracted.filter p).sort (Β· ≀ Β·) := by have h1 : (c.uncontractedList.filter p).Sorted (Β· ≀ Β·) := by @@ -237,14 +236,12 @@ lemma filter_uncontractedList (c : WickContraction n) (p : Fin n β†’ Prop) [Deci have hx := (List.toFinset_sort (Β· ≀ Β·) h2).mpr h1 rw [← hx, h3] - /-! ## uncontractedIndexEquiv -/ - /-- The equivalence between the positions of `c.uncontractedList` i.e. elements of `Fin (c.uncontractedList).length` and the finite set `c.uncontracted` considered as a finite type. -/ @@ -315,7 +312,6 @@ lemma uncontractedStatesEquiv_list_sum [AddCommMonoid Ξ±] (Ο†s : List 𝓕.State -/ - lemma uncontractedList_succAboveEmb_sorted (c : WickContraction n) (i : Fin n.succ) : ((List.map i.succAboveEmb c.uncontractedList)).Sorted (Β· ≀ Β·) := by apply fin_list_sorted_succAboveEmb_sorted