refactor: Lint
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jstoobysmith
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6c17a61989
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b0c5ed894f
8 changed files with 16 additions and 11 deletions
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@ -95,6 +95,7 @@ import HepLean.Lorentz.PauliMatrices.SelfAdjoint
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import HepLean.Lorentz.RealVector.Basic
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import HepLean.Lorentz.RealVector.Contraction
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import HepLean.Lorentz.RealVector.Modules
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import HepLean.Lorentz.RealVector.NormOne
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import HepLean.Lorentz.SL2C.Basic
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import HepLean.Lorentz.Weyl.Basic
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import HepLean.Lorentz.Weyl.Contraction
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@ -123,7 +123,6 @@ instance (M : LorentzGroup d) : Invertible M.1 where
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rw [← coe_inv]
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exact (mem_iff_self_mul_dual.mp M.2)
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@[simp]
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lemma subtype_inv_mul : (Subtype.val Λ)⁻¹ * (Subtype.val Λ) = 1 := by
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trans Subtype.val (Λ⁻¹ * Λ)
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· rw [← coe_inv]
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@ -131,7 +130,6 @@ lemma subtype_inv_mul : (Subtype.val Λ)⁻¹ * (Subtype.val Λ) = 1 := by
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· rw [inv_mul_cancel Λ]
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rfl
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@[simp]
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lemma subtype_mul_inv : (Subtype.val Λ) * (Subtype.val Λ)⁻¹ = 1 := by
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trans Subtype.val (Λ * Λ⁻¹)
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· rw [← coe_inv]
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@ -145,7 +145,7 @@ lemma toMatrix_apply (u v : FuturePointing d) (μ ν : Fin 1 ⊕ Fin d) :
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rw [contrContrContractField.matrix_apply_stdBasis (Λ := toMatrix u v) μ ν, toMatrix_mulVec]
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simp only [genBoost, genBoostAux₁, genBoostAux₂, smul_add, neg_smul, LinearMap.add_apply,
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LinearMap.id_apply, LinearMap.coe_mk, AddHom.coe_mk, contrContrContractField.basis_left,
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map_add, map_smul, map_neg, toField_apply, mul_eq_mul_left_iff]
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map_add, map_smul, map_neg, mul_eq_mul_left_iff]
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ring_nf
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simp only [Pi.add_apply, Action.instMonoidalCategory_tensorObj_V,
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Action.instMonoidalCategory_tensorUnit_V, CategoryTheory.Equivalence.symm_inverse,
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@ -61,9 +61,6 @@ def Co (d : ℕ) : Rep ℝ (LorentzGroup d) := Rep.of CoMod.rep
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open CategoryTheory.MonoidalCategory
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def toField (d : ℕ) : (𝟙_ (Rep ℝ ↑(LorentzGroup d))) →ₗ[ℝ] ℝ := LinearMap.id
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lemma toField_apply {d : ℕ} (a : 𝟙_ (Rep ℝ ↑(LorentzGroup d))) : toField d a = a := rfl
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/-!
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## Isomorphism between contravariant and covariant Lorentz vectors
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@ -200,7 +200,7 @@ lemma action_tmul (g : LorentzGroup d) : ⟪(Contr d).ρ g x, (Contr d).ρ g y
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rfl
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lemma as_sum : ⟪x, y⟫ₘ = x.val (Sum.inl 0) * y.val (Sum.inl 0) -
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∑ i, x.val (Sum.inr i) * y.val (Sum.inr i) := by
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∑ i, x.val (Sum.inr i) * y.val (Sum.inr i) := by
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rw [contrContrContract_hom_tmul]
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simp only [dotProduct, minkowskiMatrix, LieAlgebra.Orthogonal.indefiniteDiagonal, mulVec_diagonal,
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Fintype.sum_sum_type, Finset.univ_unique, Fin.default_eq_zero, Fin.isValue, Sum.elim_inl,
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@ -214,7 +214,6 @@ lemma as_sum_toSpace : ⟪x, y⟫ₘ = x.val (Sum.inl 0) * y.val (Sum.inl 0) -
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rw [as_sum]
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rfl
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@[simp]
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lemma stdBasis_inl {d : ℕ} :
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⟪@ContrMod.stdBasis d (Sum.inl 0), ContrMod.stdBasis (Sum.inl 0)⟫ₘ = (1 : ℝ) := by
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rw [as_sum]
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@ -136,9 +136,11 @@ lemma stdBasis_decomp (v : ContrMod d) : v = ∑ i, v.toFin1dℝ i • stdBasis
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-/
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/-- Multiplication of a matrix with a vector in `ContrMod`. -/
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abbrev mulVec (M : Matrix (Fin 1 ⊕ Fin d) (Fin 1 ⊕ Fin d) ℝ) (v : ContrMod d) :
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ContrMod d := Matrix.toLinAlgEquiv stdBasis M v
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/-- Multiplication of a matrix with a vector in `ContrMod`. -/
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scoped[Lorentz] infixr:73 " *ᵥ " => ContrMod.mulVec
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@[simp]
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@ -173,6 +175,8 @@ lemma mulVec_mulVec (M N : Matrix (Fin 1 ⊕ Fin d) (Fin 1 ⊕ Fin d) ℝ) (v :
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(Not the Minkowski norm, but the norm of a vector in `ContrℝModule d`.)
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-/
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/-- A `NormedAddCommGroup` structure on `ContrMod`. This is not an instance, as we
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don't want it to be applied always. -/
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def norm : NormedAddCommGroup (ContrMod d) where
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norm v := ‖v.val‖₊
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dist_self x := Pi.normedAddCommGroup.dist_self x.val
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@ -180,6 +184,8 @@ def norm : NormedAddCommGroup (ContrMod d) where
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dist_comm x y := Pi.normedAddCommGroup.dist_comm x.val y.val
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eq_of_dist_eq_zero {x y} := fun h => ext (MetricSpace.eq_of_dist_eq_zero h)
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/-- The underlying space part of a `ContrMod` formed by removing the first element.
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A better name for this might be `tail`. -/
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def toSpace (v : ContrMod d) : EuclideanSpace ℝ (Fin d) := v.val ∘ Sum.inr
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/-!
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@ -368,9 +374,11 @@ lemma stdBasis_decomp (v : CoMod d) : v = ∑ i, v.toFin1dℝ i • stdBasis i :
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-/
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/-- Multiplication of a matrix with a vector in `CoMod`. -/
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abbrev mulVec (M : Matrix (Fin 1 ⊕ Fin d) (Fin 1 ⊕ Fin d) ℝ) (v : CoMod d) :
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CoMod d := Matrix.toLinAlgEquiv stdBasis M v
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/-- Multiplication of a matrix with a vector in `CoMod`. -/
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scoped[Lorentz] infixr:73 " *ᵥ " => CoMod.mulVec
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@[simp]
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@ -208,7 +208,7 @@ lemma metric_reflect_not_mem_not_mem (h : v ∉ FuturePointing d) (hw : w ∉ Fu
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simp [neg, neg_tmul, tmul_neg]
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lemma metric_reflect_mem_not_mem (h : v ∈ FuturePointing d) (hw : w ∉ FuturePointing d) :
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⟪v.val, (Contr d).ρ LorentzGroup.parity w.1⟫ₘ ≤ 0 := by
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⟪v.val, (Contr d).ρ LorentzGroup.parity w.1⟫ₘ ≤ 0 := by
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rw [show (0 : ℝ) = - 0 from zero_eq_neg.mpr rfl, le_neg]
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have h1 := metric_reflect_mem_mem h ((not_mem_iff_neg w).mp hw)
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apply le_of_le_of_eq h1 ?_
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@ -248,8 +248,8 @@ noncomputable def pathFromTime (u : FuturePointing d) : Path timeVecNormOneFutur
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| Sum.inr i => t * u.1.1.toSpace i},
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by
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rw [NormOne.mem_iff, contrContrContractField.as_sum_toSpace]
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simp only [ContrMod.toSpace, Function.comp_apply, PiLp.inner_apply, RCLike.inner_apply, map_mul,
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conj_trivial]
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simp only [ContrMod.toSpace, Function.comp_apply, PiLp.inner_apply, RCLike.inner_apply,
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map_mul, conj_trivial]
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rw [Real.mul_self_sqrt, ← @real_inner_self_eq_norm_sq, @PiLp.inner_apply]
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· simp only [Function.comp_apply, RCLike.inner_apply, conj_trivial]
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refine Eq.symm (eq_sub_of_add_eq (congrArg (HAdd.hAdd _) ?_))
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@ -76,6 +76,8 @@ lemma toLinearMapSelfAdjointMatrix_det (M : SL(2, ℂ)) (A : selfAdjoint (Matrix
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selfAdjoint.mem_iff, det_conjTranspose, det_mul, det_one, RingHom.id_apply]
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simp only [SpecialLinearGroup.det_coe, one_mul, star_one, mul_one]
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/-- The monoid homomorphisms from `SL(2, ℂ)` to matrices indexed by `Fin 1 ⊕ Fin 3`
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formed by the action `M A Mᴴ`. -/
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def toMatrix : SL(2, ℂ) →* Matrix (Fin 1 ⊕ Fin 3) (Fin 1 ⊕ Fin 3) ℝ where
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toFun M := LinearMap.toMatrix PauliMatrix.σSAL PauliMatrix.σSAL (toLinearMapSelfAdjointMatrix M)
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map_one' := by
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