refactor: Lint

This commit is contained in:
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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@ -55,7 +55,7 @@ def leftBasis : Basis (Fin 2) leftHanded := Basis.ofEquivFun
lemma leftBasis_ρ_apply (M : SL(2,)) (i j : Fin 2) :
(LinearMap.toMatrix leftBasis leftBasis) (leftHanded.ρ M) i j = M.1 i j := by
rw [LinearMap.toMatrix_apply]
simp [leftBasis]
simp only [leftBasis, Basis.coe_ofEquivFun, Basis.ofEquivFun_repr_apply]
change (M.1 *ᵥ (Pi.single j 1)) i = _
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.
Authors: Joseph Tooby-Smith
-/
import HepLean.SpaceTime.WeylFermion.Basic
import LLMlean
/-!
# Contraction of Weyl fermions

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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) := !![0, 1; -1, 0]
lemma comm_metricRaw (M : SL(2,)) : M.1 * metricRaw = metricRaw * (M.1⁻¹)ᵀ := by
@ -91,7 +92,7 @@ def leftMetric : 𝟙_ (Rep SL(2,)) ⟶ 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 SL(2,)) ⟶ 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]

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@ -81,7 +81,7 @@ def altLeftLeftUnit : 𝟙_ (Rep SL(2,)) ⟶ altLeftHanded ⊗ leftHanded
(TensorProduct.map (altLeftHanded.ρ M) (leftHanded.ρ M)) (x' • altLeftLeftUnitVal)
simp only [Action.instMonoidalCategory_tensorObj_V, _root_.map_smul]
apply congrArg
simp [altLeftLeftUnitVal]
simp only [Action.instMonoidalCategory_tensorObj_V, altLeftLeftUnitVal]
erw [altLeftLeftToMatrix_ρ_symm]
apply congrArg
simp only [mul_one, ← transpose_mul, SpecialLinearGroup.det_coe, isUnit_iff_ne_zero, ne_eq,
@ -154,7 +154,7 @@ def altRightRightUnit : 𝟙_ (Rep SL(2,)) ⟶ altRightHanded ⊗ rightHa
(TensorProduct.map (altRightHanded.ρ M) (rightHanded.ρ M)) (x' • altRightRightUnitVal)
simp only [Action.instMonoidalCategory_tensorObj_V, _root_.map_smul]
apply congrArg
simp [altRightRightUnitVal]
simp only [Action.instMonoidalCategory_tensorObj_V, altRightRightUnitVal]
erw [altRightRightToMatrix_ρ_symm]
apply congrArg
simp only [mul_one, RCLike.star_def]