DibyashanuPati/PhysLean
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

chore: bump toolchain to v4.15.0

Browse source 
#281 adapt code to v4.15.0 and fix long heartbeats, e.g., toDualRep_apply_eq_contrOneTwoLeft.

---------

Co-authored-by: jstoobysmith <72603918+jstoobysmith@users.noreply.github.com>
This commit is contained in:
KUO-TSAN HSU (Gordon) 2025-01-20 15:42:53 +08:00 • committed by GitHub
parent 6e31281a5b
commit 656a3e422f
No known key found for this signature in database
GPG key ID: B5690EEEBB952194
49 changed files with 484 additions and 472 deletions
Download patch file Download diff file Expand all files Collapse all files

36
HepLean/Lorentz/ComplexVector/Unit.lean
View file

@ -41,7 +41,7 @@ lemma contrCoUnitVal_expand_tmul : contrCoUnitVal =
`𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ complexContr ⊗ complexCo`, manifesting the invaraince under
the `SL(2, ℂ)` action. -/
def contrCoUnit : 𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ complexContr ⊗ complexCo where
hom := {
hom := ModuleCat.ofHom {
toFun := fun a =>
let a' : ℂ := a
a' • contrCoUnitVal,
@ -51,13 +51,13 @@ def contrCoUnit : 𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ complexContr ⊗ complexCo where
simp only [smul_smul]
rfl}
comm M := by
ext x : 2
refine ModuleCat.hom_ext ?_
refine LinearMap.ext fun x : ℂ => ?_
simp only [Action.instMonoidalCategory_tensorObj_V, Action.instMonoidalCategory_tensorUnit_V,
Action.tensorUnit_ρ', CategoryTheory.Category.id_comp, Action.tensor_ρ', ModuleCat.coe_comp,
Action.tensorUnit_ρ', CategoryTheory.Category.id_comp, Action.tensor_ρ', ModuleCat.hom_comp,
Function.comp_apply]
let x' : ℂ := x
change x' • contrCoUnitVal =
(TensorProduct.map (complexContr.ρ M) (complexCo.ρ M)) (x' • contrCoUnitVal)
change x • contrCoUnitVal =
(TensorProduct.map (complexContr.ρ M) (complexCo.ρ M)) (x • contrCoUnitVal)
simp only [Action.instMonoidalCategory_tensorObj_V, _root_.map_smul]
apply congrArg
simp only [Action.instMonoidalCategory_tensorObj_V, contrCoUnitVal]
@ -66,9 +66,8 @@ def contrCoUnit : 𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ complexContr ⊗ complexCo where
simp
lemma contrCoUnit_apply_one : contrCoUnit.hom (1 : ℂ) = contrCoUnitVal := by
change contrCoUnit.hom.toFun (1 : ℂ) = contrCoUnitVal
simp only [Action.instMonoidalCategory_tensorObj_V, Action.instMonoidalCategory_tensorUnit_V,
contrCoUnit, AddHom.toFun_eq_coe, AddHom.coe_mk, one_smul]
change contrCoUnit.hom.hom.toFun (1 : ℂ) = contrCoUnitVal
simp only [contrCoUnit, one_smul]
/-- The co-contra unit for complex lorentz vectors. Usually denoted `δᵢⁱ`. -/
def coContrUnitVal : (complexCo ⊗ complexContr).V :=
@ -92,7 +91,7 @@ lemma coContrUnitVal_expand_tmul : coContrUnitVal =
`𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ complexCo ⊗ complexContr`, manifesting the invaraince under
the `SL(2, ℂ)` action. -/
def coContrUnit : 𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ complexCo ⊗ complexContr where
hom := {
hom := ModuleCat.ofHom {
toFun := fun a =>
let a' : ℂ := a
a' • coContrUnitVal,
@ -102,13 +101,13 @@ def coContrUnit : 𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ complexCo ⊗ complexContr where
simp only [smul_smul]
rfl}
comm M := by
ext x : 2
refine ModuleCat.hom_ext ?_
refine LinearMap.ext fun x : ℂ => ?_
simp only [Action.instMonoidalCategory_tensorObj_V, Action.instMonoidalCategory_tensorUnit_V,
Action.tensorUnit_ρ', CategoryTheory.Category.id_comp, Action.tensor_ρ', ModuleCat.coe_comp,
Action.tensorUnit_ρ', CategoryTheory.Category.id_comp, Action.tensor_ρ', ModuleCat.hom_comp,
Function.comp_apply]
let x' : ℂ := x
change x' • coContrUnitVal =
(TensorProduct.map (complexCo.ρ M) (complexContr.ρ M)) (x' • coContrUnitVal)
change x • coContrUnitVal =
(TensorProduct.map (complexCo.ρ M) (complexContr.ρ M)) (x • coContrUnitVal)
simp only [Action.instMonoidalCategory_tensorObj_V, _root_.map_smul]
apply congrArg
simp only [Action.instMonoidalCategory_tensorObj_V, coContrUnitVal]
@ -119,9 +118,8 @@ def coContrUnit : 𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ complexCo ⊗ complexContr where
simp
lemma coContrUnit_apply_one : coContrUnit.hom (1 : ℂ) = coContrUnitVal := by
change coContrUnit.hom.toFun (1 : ℂ) = coContrUnitVal
simp only [Action.instMonoidalCategory_tensorObj_V, Action.instMonoidalCategory_tensorUnit_V,
coContrUnit, AddHom.toFun_eq_coe, AddHom.coe_mk, one_smul]
change coContrUnit.hom.hom.toFun (1 : ℂ) = coContrUnitVal
simp only [coContrUnit, one_smul]
/-!
## Contraction of the units
@ -153,7 +151,7 @@ lemma contr_contrCoUnit (x : complexCo) :
repeat rw (config := { transparency := .instances }) [h1'']
repeat rw [coContrContraction_basis']
simp only [Fin.isValue, leftUnitor, ModuleCat.MonoidalCategory.leftUnitor, ModuleCat.of_coe,
CategoryTheory.Iso.trans_hom, LinearEquiv.toModuleIso_hom, ModuleCat.ofSelfIso_hom,
CategoryTheory.Iso.trans_hom, LinearEquiv.toModuleIso_hom_hom, ModuleCat.ofSelfIso_hom,
CategoryTheory.Category.comp_id, Action.instMonoidalCategory_tensorUnit_V, ↓reduceIte,
reduceCtorEq, zero_tmul, map_zero, smul_zero, add_zero, Sum.inr.injEq, one_ne_zero,
Fin.reduceEq, zero_add, zero_ne_one]