refactor: Lint
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4 changed files with 6 additions and 6 deletions
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@ -55,7 +55,7 @@ def leftBasis : Basis (Fin 2) ℂ leftHanded := Basis.ofEquivFun
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lemma leftBasis_ρ_apply (M : SL(2,ℂ)) (i j : Fin 2) :
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(LinearMap.toMatrix leftBasis leftBasis) (leftHanded.ρ M) i j = M.1 i j := by
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rw [LinearMap.toMatrix_apply]
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simp [leftBasis]
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simp only [leftBasis, Basis.coe_ofEquivFun, Basis.ofEquivFun_repr_apply]
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change (M.1 *ᵥ (Pi.single j 1)) i = _
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simp only [mulVec_single, mul_one]
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@ -4,7 +4,6 @@ Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Joseph Tooby-Smith
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-/
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import HepLean.SpaceTime.WeylFermion.Basic
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import LLMlean
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/-!
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# Contraction of Weyl fermions
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@ -26,6 +26,7 @@ open Complex
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open TensorProduct
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open CategoryTheory.MonoidalCategory
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/-- The raw `2x2` matrix corresponding to the metric for fermions. -/
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def metricRaw : Matrix (Fin 2) (Fin 2) ℂ := !![0, 1; -1, 0]
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lemma comm_metricRaw (M : SL(2,ℂ)) : M.1 * metricRaw = metricRaw * (M.1⁻¹)ᵀ := by
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@ -91,7 +92,7 @@ def leftMetric : 𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ leftHanded ⊗ leftHanded where
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(TensorProduct.map (leftHanded.ρ M) (leftHanded.ρ M)) (x' • leftMetricVal)
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simp only [Action.instMonoidalCategory_tensorObj_V, _root_.map_smul]
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apply congrArg
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simp [leftMetricVal]
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simp only [Action.instMonoidalCategory_tensorObj_V, leftMetricVal, map_neg, neg_inj]
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erw [leftLeftToMatrix_ρ_symm]
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apply congrArg
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rw [comm_metricRaw, mul_assoc, ← @transpose_mul]
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@ -124,7 +125,7 @@ def altLeftMetric : 𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ altLeftHanded ⊗ altLeftHande
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(TensorProduct.map (altLeftHanded.ρ M) (altLeftHanded.ρ M)) (x' • altLeftMetricVal)
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simp only [Action.instMonoidalCategory_tensorObj_V, _root_.map_smul]
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apply congrArg
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simp [altLeftMetricVal]
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simp only [Action.instMonoidalCategory_tensorObj_V, altLeftMetricVal]
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erw [altLeftaltLeftToMatrix_ρ_symm]
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apply congrArg
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rw [← metricRaw_comm, mul_assoc]
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@ -81,7 +81,7 @@ def altLeftLeftUnit : 𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ altLeftHanded ⊗ leftHanded
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(TensorProduct.map (altLeftHanded.ρ M) (leftHanded.ρ M)) (x' • altLeftLeftUnitVal)
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simp only [Action.instMonoidalCategory_tensorObj_V, _root_.map_smul]
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apply congrArg
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simp [altLeftLeftUnitVal]
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simp only [Action.instMonoidalCategory_tensorObj_V, altLeftLeftUnitVal]
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erw [altLeftLeftToMatrix_ρ_symm]
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apply congrArg
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simp only [mul_one, ← transpose_mul, SpecialLinearGroup.det_coe, isUnit_iff_ne_zero, ne_eq,
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@ -154,7 +154,7 @@ def altRightRightUnit : 𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ altRightHanded ⊗ rightHa
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(TensorProduct.map (altRightHanded.ρ M) (rightHanded.ρ M)) (x' • altRightRightUnitVal)
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simp only [Action.instMonoidalCategory_tensorObj_V, _root_.map_smul]
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apply congrArg
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simp [altRightRightUnitVal]
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simp only [Action.instMonoidalCategory_tensorObj_V, altRightRightUnitVal]
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erw [altRightRightToMatrix_ρ_symm]
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apply congrArg
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simp only [mul_one, RCLike.star_def]
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