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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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18
HepLean/PerturbationTheory/Algebras/FieldOpAlgebra/WicksTheoremNormal.lean
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@ -20,7 +20,7 @@ namespace FieldOpAlgebra
open WickContraction
open EqTimeOnly
lemma timeOrder_ofFieldOpList_eqTimeOnly (φs : List 𝓕.States) :
lemma timeOrder_ofFieldOpList_eqTimeOnly (φs : List 𝓕.FieldOp) :
timeOrder (ofFieldOpList φs) = ∑ (φsΛ : {φsΛ // φsΛ.EqTimeOnly (φs := φs)}),
φsΛ.1.sign • φsΛ.1.timeContract.1 * 𝓣(𝓝(ofFieldOpList [φsΛ.1]ᵘᶜ)) := by
rw [static_wick_theorem φs]
@ -43,7 +43,7 @@ lemma timeOrder_ofFieldOpList_eqTimeOnly (φs : List 𝓕.States) :
exact x.2
exact x.2
lemma timeOrder_ofFieldOpList_eq_eqTimeOnly_empty (φs : List 𝓕.States) :
lemma timeOrder_ofFieldOpList_eq_eqTimeOnly_empty (φs : List 𝓕.FieldOp) :
timeOrder (ofFieldOpList φs) = 𝓣(𝓝(ofFieldOpList φs)) +
∑ (φsΛ : {φsΛ // φsΛ.EqTimeOnly (φs := φs) ∧ φsΛ ≠ empty}),
φsΛ.1.sign • φsΛ.1.timeContract.1 * 𝓣(𝓝(ofFieldOpList [φsΛ.1]ᵘᶜ)) := by
@ -70,14 +70,14 @@ lemma timeOrder_ofFieldOpList_eq_eqTimeOnly_empty (φs : List 𝓕.States) :
rw [← e2.symm.sum_comp]
rfl
lemma normalOrder_timeOrder_ofFieldOpList_eq_eqTimeOnly_empty (φs : List 𝓕.States) :
lemma normalOrder_timeOrder_ofFieldOpList_eq_eqTimeOnly_empty (φs : List 𝓕.FieldOp) :
𝓣(𝓝(ofFieldOpList φs)) = 𝓣(ofFieldOpList φs) -
∑ (φsΛ : {φsΛ // φsΛ.EqTimeOnly (φs := φs) ∧ φsΛ ≠ empty}),
φsΛ.1.sign • φsΛ.1.timeContract.1 * 𝓣(𝓝(ofFieldOpList [φsΛ.1]ᵘᶜ)) := by
rw [timeOrder_ofFieldOpList_eq_eqTimeOnly_empty]
simp
lemma normalOrder_timeOrder_ofFieldOpList_eq_haveEqTime_sum_not_haveEqTime (φs : List 𝓕.States) :
lemma normalOrder_timeOrder_ofFieldOpList_eq_haveEqTime_sum_not_haveEqTime (φs : List 𝓕.FieldOp) :
𝓣(𝓝(ofFieldOpList φs)) = (∑ (φsΛ : {φsΛ : WickContraction φs.length // ¬ HaveEqTime φsΛ}),
φsΛ.1.sign • φsΛ.1.timeContract.1 * 𝓝(ofFieldOpList [φsΛ.1]ᵘᶜ))
+ (∑ (φsΛ : {φsΛ : WickContraction φs.length // HaveEqTime φsΛ}),
@ -93,7 +93,7 @@ lemma normalOrder_timeOrder_ofFieldOpList_eq_haveEqTime_sum_not_haveEqTime (φs
Equiv.sumCompl_apply_inl, Equiv.sumCompl_apply_inr, ne_eq, sub_left_inj, e1]
rw [add_comm]
lemma haveEqTime_wick_sum_eq_split (φs : List 𝓕.States) :
lemma haveEqTime_wick_sum_eq_split (φs : List 𝓕.FieldOp) :
(∑ (φsΛ : {φsΛ : WickContraction φs.length // HaveEqTime φsΛ}),
φsΛ.1.sign • φsΛ.1.timeContract.1 * 𝓝(ofFieldOpList [φsΛ.1]ᵘᶜ)) =
∑ (φsΛ : {φsΛ // φsΛ.EqTimeOnly (φs := φs) ∧ φsΛ ≠ empty}),
@ -122,7 +122,7 @@ lemma haveEqTime_wick_sum_eq_split (φs : List 𝓕.States) :
congr 1
rw [@join_uncontractedListGet]
lemma normalOrder_timeOrder_ofFieldOpList_eq_not_haveEqTime_sub_inductive (φs : List 𝓕.States) :
lemma normalOrder_timeOrder_ofFieldOpList_eq_not_haveEqTime_sub_inductive (φs : List 𝓕.FieldOp) :
𝓣(𝓝(ofFieldOpList φs)) = (∑ (φsΛ : {φsΛ : WickContraction φs.length // ¬ HaveEqTime φsΛ}),
φsΛ.1.sign • φsΛ.1.timeContract.1 * 𝓝(ofFieldOpList [φsΛ.1]ᵘᶜ))
+ ∑ (φsΛ : {φsΛ // φsΛ.EqTimeOnly (φs := φs) ∧ φsΛ ≠ empty}),
@ -142,9 +142,9 @@ lemma normalOrder_timeOrder_ofFieldOpList_eq_not_haveEqTime_sub_inductive (φs :
rw [← smul_sub, ← mul_sub]
lemma wicks_theorem_normal_order_empty : 𝓣(𝓝(ofFieldOpList [])) =
∑ (φsΛ : {φsΛ : WickContraction ([] : List 𝓕.States).length // ¬ HaveEqTime φsΛ}),
∑ (φsΛ : {φsΛ : WickContraction ([] : List 𝓕.FieldOp).length // ¬ HaveEqTime φsΛ}),
φsΛ.1.sign • φsΛ.1.timeContract.1 * 𝓝(ofFieldOpList [φsΛ.1]ᵘᶜ) := by
let e2 : {φsΛ : WickContraction ([] : List 𝓕.States).length // ¬ HaveEqTime φsΛ} ≃ Unit :=
let e2 : {φsΛ : WickContraction ([] : List 𝓕.FieldOp).length // ¬ HaveEqTime φsΛ} ≃ Unit :=
{
toFun := fun x => (),
invFun := fun x => ⟨empty, by simp⟩,
@ -181,7 +181,7 @@ Wicks theorem for normal ordering followed by time-ordering, states that
for those Wick contraction `φsΛ` which do not have any equal time contractions.
This is compared to the ordinary Wicks theorem which sums over all Wick contractions.
-/
theorem wicks_theorem_normal_order : (φs : List 𝓕.States) →
theorem wicks_theorem_normal_order : (φs : List 𝓕.FieldOp) →
𝓣(𝓝(ofFieldOpList φs)) = ∑ (φsΛ : {φsΛ : WickContraction φs.length // ¬ HaveEqTime φsΛ}),
φsΛ.1.sign • φsΛ.1.timeContract.1 * 𝓝(ofFieldOpList [φsΛ.1]ᵘᶜ)
| [] => wicks_theorem_normal_order_empty