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refactor: Lint

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jstoobysmith 2024-10-15 11:53:24 +00:00
parent f72d69e2ba
commit 12dd1fbbac
4 changed files with 6 additions and 6 deletions
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5
HepLean/SpaceTime/WeylFermion/Metric.lean
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@ -26,6 +26,7 @@ open Complex
open TensorProduct
open CategoryTheory.MonoidalCategory
/-- The raw `2x2` matrix corresponding to the metric for fermions. -/
def metricRaw : Matrix (Fin 2) (Fin 2) ℂ := !![0, 1; -1, 0]
lemma comm_metricRaw (M : SL(2,ℂ)) : M.1 * metricRaw = metricRaw * (M.1⁻¹)ᵀ := by
@ -91,7 +92,7 @@ def leftMetric : 𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ leftHanded ⊗ leftHanded where
(TensorProduct.map (leftHanded.ρ M) (leftHanded.ρ M)) (x' • leftMetricVal)
simp only [Action.instMonoidalCategory_tensorObj_V, _root_.map_smul]
apply congrArg
simp [leftMetricVal]
simp only [Action.instMonoidalCategory_tensorObj_V, leftMetricVal, map_neg, neg_inj]
erw [leftLeftToMatrix_ρ_symm]
apply congrArg
rw [comm_metricRaw, mul_assoc, ← @transpose_mul]
@ -124,7 +125,7 @@ def altLeftMetric : 𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ altLeftHanded ⊗ altLeftHande
(TensorProduct.map (altLeftHanded.ρ M) (altLeftHanded.ρ M)) (x' • altLeftMetricVal)
simp only [Action.instMonoidalCategory_tensorObj_V, _root_.map_smul]
apply congrArg
simp [altLeftMetricVal]
simp only [Action.instMonoidalCategory_tensorObj_V, altLeftMetricVal]
erw [altLeftaltLeftToMatrix_ρ_symm]
apply congrArg
rw [← metricRaw_comm, mul_assoc]