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feat: More fixes

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This commit is contained in:
jstoobysmith 2024-11-02 08:50:17 +00:00
parent 4df8663cbc
commit c9c9047a0c
31 changed files with 134 additions and 124 deletions
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18
HepLean/SpaceTime/LorentzVector/Complex/Basic.lean
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@ -94,25 +94,25 @@ def complexCoBasisFin4 : Basis (Fin 4) ℂ complexCo :=
/-- The semilinear map including real Lorentz vectors into complex contravariant
lorentz vectors. -/
def inclCongrRealLorentz : LorentzVector 3 →ₛₗ[Complex.ofReal] complexContr where
def inclCongrRealLorentz : LorentzVector 3 →ₛₗ[Complex.ofRealHom] complexContr where
toFun v := {val := ofReal ∘ v}
map_add' x y := by
apply Lorentz.ContrℂModule.ext
rw [Lorentz.ContrℂModule.val_add]
funext i
simp only [Function.comp_apply, ofReal_eq_coe, Pi.add_apply]
simp only [Function.comp_apply, ofRealHom_eq_coe, Pi.add_apply]
change ofReal (x i + y i) = _
simp only [ofReal_eq_coe, ofReal_add]
simp only [ofRealHom_eq_coe, ofReal_add]
map_smul' c x := by
apply Lorentz.ContrℂModule.ext
rw [Lorentz.ContrℂModule.val_smul]
funext i
simp only [Function.comp_apply, ofReal_eq_coe, Pi.smul_apply]
simp only [Function.comp_apply, ofRealHom_eq_coe, Pi.smul_apply]
change ofReal (c • x i) = _
simp only [smul_eq_mul, ofReal_eq_coe, ofReal_mul]
simp only [smul_eq_mul, ofRealHom_eq_coe, ofReal_mul]
lemma inclCongrRealLorentz_val (v : LorentzVector 3) :
(inclCongrRealLorentz v).val = ofReal ∘ v := rfl
(inclCongrRealLorentz v).val = ofRealHom ∘ v := rfl
lemma complexContrBasis_of_real (i : Fin 1 ⊕ Fin 3) :
(complexContrBasis i) = inclCongrRealLorentz (LorentzVector.stdBasis i) := by
@ -120,10 +120,10 @@ lemma complexContrBasis_of_real (i : Fin 1 ⊕ Fin 3) :
simp only [complexContrBasis, Basis.coe_ofEquivFun, inclCongrRealLorentz, LorentzVector.stdBasis,
LinearMap.coe_mk, AddHom.coe_mk]
ext j
simp only [Function.comp_apply, ofReal_eq_coe]
simp only [Function.comp_apply, ofRealHom_eq_coe]
erw [Pi.basisFun_apply]
change (Pi.single i 1) j = _
exact Eq.symm (Pi.apply_single (fun _ => ofReal') (congrFun rfl) i 1 j)
exact Eq.symm (Pi.apply_single (fun _ => ofRealHom) (congrFun rfl) i 1 j)
lemma inclCongrRealLorentz_ρ (M : SL(2, ℂ)) (v : LorentzVector 3) :
(complexContr.ρ M) (inclCongrRealLorentz v) =
@ -143,7 +143,7 @@ lemma SL2CRep_ρ_basis (M : SL(2, ℂ)) (i : Fin 1 ⊕ Fin 3) :
rw [complexContrBasis_of_real, inclCongrRealLorentz_ρ, SL2C.repLorentzVector_stdBasis, map_sum]
apply congrArg
funext j
simp only [LinearMap.map_smulₛₗ, ofReal_eq_coe, coe_smul]
simp only [LinearMap.map_smulₛₗ, ofRealHom_eq_coe, coe_smul]
rw [complexContrBasis_of_real]
end Lorentz

8
HepLean/SpaceTime/LorentzVector/Complex/Metric.lean
View file

@ -24,7 +24,7 @@ namespace Lorentz
/-- The metric `ηᵃᵃ` as an element of `(complexContr ⊗ complexContr).V`. -/
def contrMetricVal : (complexContr ⊗ complexContr).V :=
contrContrToMatrix.symm ((@minkowskiMatrix 3).map ofReal)
contrContrToMatrix.symm ((@minkowskiMatrix 3).map ofRealHom)
/-- The expansion of `contrMetricVal` into basis vectors. -/
lemma contrMetricVal_expand_tmul : contrMetricVal =
@ -34,7 +34,7 @@ lemma contrMetricVal_expand_tmul : contrMetricVal =
- complexContrBasis (Sum.inr 2) ⊗ₜ[ℂ] complexContrBasis (Sum.inr 2) := by
simp only [Action.instMonoidalCategory_tensorObj_V, contrMetricVal, Fin.isValue]
erw [contrContrToMatrix_symm_expand_tmul]
simp only [map_apply, ofReal_eq_coe, coe_smul, Fintype.sum_sum_type, Finset.univ_unique,
simp only [map_apply, ofRealHom_eq_coe, coe_smul, Fintype.sum_sum_type, Finset.univ_unique,
Fin.default_eq_zero, Fin.isValue, Finset.sum_singleton, Fin.sum_univ_three, ne_eq, reduceCtorEq,
not_false_eq_true, minkowskiMatrix.off_diag_zero, zero_smul, add_zero, zero_add, Sum.inr.injEq,
zero_ne_one, Fin.reduceEq, one_ne_zero]
@ -77,7 +77,7 @@ lemma contrMetric_apply_one : contrMetric.hom (1 : ℂ) = contrMetricVal := by
/-- The metric `ηᵢᵢ` as an element of `(complexCo ⊗ complexCo).V`. -/
def coMetricVal : (complexCo ⊗ complexCo).V :=
coCoToMatrix.symm ((@minkowskiMatrix 3).map ofReal)
coCoToMatrix.symm ((@minkowskiMatrix 3).map ofRealHom)
/-- The expansion of `coMetricVal` into basis vectors. -/
lemma coMetricVal_expand_tmul : coMetricVal =
@ -87,7 +87,7 @@ lemma coMetricVal_expand_tmul : coMetricVal =
- complexCoBasis (Sum.inr 2) ⊗ₜ[ℂ] complexCoBasis (Sum.inr 2) := by
simp only [Action.instMonoidalCategory_tensorObj_V, coMetricVal, Fin.isValue]
erw [coCoToMatrix_symm_expand_tmul]
simp only [map_apply, ofReal_eq_coe, coe_smul, Fintype.sum_sum_type, Finset.univ_unique,
simp only [map_apply, ofRealHom_eq_coe, coe_smul, Fintype.sum_sum_type, Finset.univ_unique,
Fin.default_eq_zero, Fin.isValue, Finset.sum_singleton, Fin.sum_univ_three, ne_eq, reduceCtorEq,
not_false_eq_true, minkowskiMatrix.off_diag_zero, zero_smul, add_zero, zero_add, Sum.inr.injEq,
zero_ne_one, Fin.reduceEq, one_ne_zero]