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refactor: Rename CrAnAlgebra

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jstoobysmith 2025-02-03 11:05:43 +00:00
parent 9a5676e134
commit b0735a1e13
16 changed files with 214 additions and 214 deletions
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22
HepLean/PerturbationTheory/Algebras/FieldOpAlgebra/SuperCommute.lean
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@ -3,7 +3,7 @@ Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
import HepLean.PerturbationTheory.Algebras.CrAnAlgebra.TimeOrder
import HepLean.PerturbationTheory.Algebras.FieldOpFreeAlgebra.TimeOrder
import HepLean.PerturbationTheory.Algebras.FieldOpAlgebra.Basic
/-!
@ -12,20 +12,20 @@ import HepLean.PerturbationTheory.Algebras.FieldOpAlgebra.Basic
-/
namespace FieldSpecification
open CrAnAlgebra
open FieldOpFreeAlgebra
open HepLean.List
open FieldStatistic
namespace FieldOpAlgebra
variable {𝓕 : FieldSpecification}
lemma ι_superCommuteF_eq_zero_of_ι_right_zero (a b : 𝓕.CrAnAlgebra) (h : ι b = 0) :
lemma ι_superCommuteF_eq_zero_of_ι_right_zero (a b : 𝓕.FieldOpFreeAlgebra) (h : ι b = 0) :
ι [a, b]ₛca = 0 := by
rw [superCommuteF_expand_bosonicProj_fermionicProj]
rw [ι_eq_zero_iff_ι_bosonicProj_fermonicProj_zero] at h
simp_all
lemma ι_superCommuteF_eq_zero_of_ι_left_zero (a b : 𝓕.CrAnAlgebra) (h : ι a = 0) :
lemma ι_superCommuteF_eq_zero_of_ι_left_zero (a b : 𝓕.FieldOpFreeAlgebra) (h : ι a = 0) :
ι [a, b]ₛca = 0 := by
rw [superCommuteF_expand_bosonicProj_fermionicProj]
rw [ι_eq_zero_iff_ι_bosonicProj_fermonicProj_zero] at h
@ -37,12 +37,12 @@ lemma ι_superCommuteF_eq_zero_of_ι_left_zero (a b : 𝓕.CrAnAlgebra) (h : ι
-/
lemma ι_superCommuteF_right_zero_of_mem_ideal (a b : 𝓕.CrAnAlgebra)
lemma ι_superCommuteF_right_zero_of_mem_ideal (a b : 𝓕.FieldOpFreeAlgebra)
(h : b ∈ TwoSidedIdeal.span 𝓕.fieldOpIdealSet) : ι [a, b]ₛca = 0 := by
apply ι_superCommuteF_eq_zero_of_ι_right_zero
exact (ι_eq_zero_iff_mem_ideal b).mpr h
lemma ι_superCommuteF_eq_of_equiv_right (a b1 b2 : 𝓕.CrAnAlgebra) (h : b1 ≈ b2) :
lemma ι_superCommuteF_eq_of_equiv_right (a b1 b2 : 𝓕.FieldOpFreeAlgebra) (h : b1 ≈ b2) :
ι [a, b1]ₛca = ι [a, b2]ₛca := by
rw [equiv_iff_sub_mem_ideal] at h
rw [LinearMap.sub_mem_ker_iff.mp]
@ -50,7 +50,7 @@ lemma ι_superCommuteF_eq_of_equiv_right (a b1 b2 : 𝓕.CrAnAlgebra) (h : b1
exact ι_superCommuteF_right_zero_of_mem_ideal a (b1 - b2) h
/-- The super commutor on the `FieldOpAlgebra` defined as a linear map `[a,_]ₛ`. -/
noncomputable def superCommuteRight (a : 𝓕.CrAnAlgebra) :
noncomputable def superCommuteRight (a : 𝓕.FieldOpFreeAlgebra) :
FieldOpAlgebra 𝓕 →ₗ[ℂ] FieldOpAlgebra 𝓕 where
toFun := Quotient.lift (ι.toLinearMap ∘ₗ superCommuteF a)
(ι_superCommuteF_eq_of_equiv_right a)
@ -67,13 +67,13 @@ noncomputable def superCommuteRight (a : 𝓕.CrAnAlgebra) :
rw [← map_smul, ι_apply, ι_apply]
simp
lemma superCommuteRight_apply_ι (a b : 𝓕.CrAnAlgebra) :
lemma superCommuteRight_apply_ι (a b : 𝓕.FieldOpFreeAlgebra) :
superCommuteRight a (ι b) = ι [a, b]ₛca := by rfl
lemma superCommuteRight_apply_quot (a b : 𝓕.CrAnAlgebra) :
lemma superCommuteRight_apply_quot (a b : 𝓕.FieldOpFreeAlgebra) :
superCommuteRight a ⟦b⟧= ι [a, b]ₛca := by rfl
lemma superCommuteRight_eq_of_equiv (a1 a2 : 𝓕.CrAnAlgebra) (h : a1 ≈ a2) :
lemma superCommuteRight_eq_of_equiv (a1 a2 : 𝓕.FieldOpFreeAlgebra) (h : a1 ≈ a2) :
superCommuteRight a1 = superCommuteRight a2 := by
rw [equiv_iff_sub_mem_ideal] at h
ext b
@ -114,7 +114,7 @@ noncomputable def superCommute : FieldOpAlgebra 𝓕 →ₗ[ℂ]
@[inherit_doc superCommute]
scoped[FieldSpecification.FieldOpAlgebra] notation "[" a "," b "]ₛ" => superCommute a b
lemma superCommute_eq_ι_superCommuteF (a b : 𝓕.CrAnAlgebra) :
lemma superCommute_eq_ι_superCommuteF (a b : 𝓕.FieldOpFreeAlgebra) :
[ι a, ι b]ₛ = ι [a, b]ₛca := rfl
/-!