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refactor: Lint

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jstoobysmith 2024-10-16 10:57:46 +00:00
parent 691b7e112e
commit a1d3616a18
10 changed files with 65 additions and 62 deletions
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10
HepLean/SpaceTime/SL2C/Basic.lean
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@ -144,9 +144,10 @@ lemma toLorentzGroup_eq_stdBasis (M : SL(2, ℂ)) :
(repLorentzVector M) := by rfl
lemma repLorentzVector_apply_eq_mulVec (v : LorentzVector 3) :
SL2C.repLorentzVector M v = (SL2C.toLorentzGroup M).1 *ᵥ v := by
SL2C.repLorentzVector M v = (SL2C.toLorentzGroup M).1 *ᵥ v := by
simp [toLorentzGroup]
have hv : v = (Finsupp.linearEquivFunOnFinite ℝ ℝ (Fin 1 ⊕ Fin 3)) (LorentzVector.stdBasis.repr v) := by rfl
have hv : v = (Finsupp.linearEquivFunOnFinite ℝ ℝ (Fin 1 ⊕ Fin 3))
(LorentzVector.stdBasis.repr v) := by rfl
nth_rewrite 2 [hv]
change _ = toLorentzGroup M *ᵥ (LorentzVector.stdBasis.repr v)
rw [toLorentzGroup_eq_stdBasis, LinearMap.toMatrix_mulVec_repr]
@ -159,10 +160,10 @@ lemma repSelfAdjointMatrix_basis (i : Fin 1 ⊕ Fin 3) :
rw [toLorentzGroup_eq_σSAL]
simp only [LinearMap.toMatrix_apply, Finset.univ_unique,
Fin.default_eq_zero, Fin.isValue, Finset.sum_singleton]
nth_rewrite 1 [← (Basis.sum_repr PauliMatrix.σSAL ((repSelfAdjointMatrix M) (PauliMatrix.σSAL i)))]
nth_rewrite 1 [← (Basis.sum_repr PauliMatrix.σSAL
((repSelfAdjointMatrix M) (PauliMatrix.σSAL i)))]
congr
lemma repSelfAdjointMatrix_σSA (i : Fin 1 ⊕ Fin 3) :
SL2C.repSelfAdjointMatrix M (PauliMatrix.σSA i) =
∑ j, (toLorentzGroup M⁻¹).1 i j • PauliMatrix.σSA j := by
@ -179,7 +180,6 @@ lemma repSelfAdjointMatrix_σSA (i : Fin 1 ⊕ Fin 3) :
apply congrArg
exact Eq.symm (minkowskiMetric.dual_apply_minkowskiMatrix ((toLorentzGroup M).1) i j)
lemma repLorentzVector_stdBasis (i : Fin 1 ⊕ Fin 3) :
SL2C.repLorentzVector M (LorentzVector.stdBasis i) =
∑ j, (toLorentzGroup M).1 j i • LorentzVector.stdBasis j := by