diff --git a/HepLean/Tensors/ComplexLorentz/Basis.lean b/HepLean/Tensors/ComplexLorentz/Basis.lean index a3ff81c..3acf860 100644 --- a/HepLean/Tensors/ComplexLorentz/Basis.lean +++ b/HepLean/Tensors/ComplexLorentz/Basis.lean @@ -38,7 +38,7 @@ namespace complexLorentzTensor /-- Basis vectors for complex Lorentz tensors. -/ def basisVector {n : ℕ} (c : Fin n → complexLorentzTensor.C) - (b : Π j, Fin (complexLorentzTensor.repDim (c j))) : + (b : Π j, Fin (complexLorentzTensor.repDim (c j))) : complexLorentzTensor.F.obj (OverColor.mk c) := PiTensorProduct.tprod ℂ (fun i => complexLorentzTensor.basis (c i) (b i)) diff --git a/HepLean/Tensors/ComplexLorentz/PauliContr.lean b/HepLean/Tensors/ComplexLorentz/PauliContr.lean index 4424299..d65380d 100644 --- a/HepLean/Tensors/ComplexLorentz/PauliContr.lean +++ b/HepLean/Tensors/ComplexLorentz/PauliContr.lean @@ -237,9 +237,9 @@ private lemma pauliMatrix_lower_basis_expand_prod' {n : ℕ} {c : Fin n → comp exact pauliMatrix_lower_basis_expand_prod _ lemma pauliMatrix_contract_pauliMatrix_aux : - {Lorentz.coMetric | μ ν ⊗ PauliMatrix.asConsTensor | μ α β ⊗ + {Lorentz.coMetric | μ ν ⊗ PauliMatrix.asConsTensor | μ α β ⊗ PauliMatrix.asConsTensor | ν α' β'}ᵀ.tensor - = ((tensorNode + = ((tensorNode ((basisVector pauliMatrixContrPauliMatrixMap fun | 0 => 0 | 1 => 0 | 2 => 0 | 3 => 0) + basisVector pauliMatrixContrPauliMatrixMap fun | 0 => 0 | 1 => 0 | 2 => 1 | 3 => 1)).add ((tensorNode @@ -310,8 +310,8 @@ lemma pauliMatrix_contract_pauliMatrix_aux : pauliMatrix_contr_lower_3_1_1] lemma pauliMatrix_contract_pauliMatrix_expand : - {Lorentz.coMetric | μ ν ⊗ PauliMatrix.asConsTensor | μ α β ⊗ - PauliMatrix.asConsTensor | ν α' β'}ᵀ.tensor = + {Lorentz.coMetric | μ ν ⊗ PauliMatrix.asConsTensor | μ α β ⊗ + PauliMatrix.asConsTensor | ν α' β'}ᵀ.tensor = 2 • basisVector pauliMatrixContrPauliMatrixMap (fun | 0 => 0 | 1 => 0 | 2 => 1 | 3 => 1) + 2 • basisVector pauliMatrixContrPauliMatrixMap (fun | 0 => 1 | 1 => 1 | 2 => 0 | 3 => 0) - 2 • basisVector pauliMatrixContrPauliMatrixMap (fun | 0 => 0 | 1 => 1 | 2 => 1 | 3 => 0) diff --git a/HepLean/Tensors/ComplexLorentz/PauliLower.lean b/HepLean/Tensors/ComplexLorentz/PauliLower.lean index f801f10..d84422e 100644 --- a/HepLean/Tensors/ComplexLorentz/PauliLower.lean +++ b/HepLean/Tensors/ComplexLorentz/PauliLower.lean @@ -139,7 +139,7 @@ lemma pauliMatrix_contr_down_3 : fin_cases k <;> rfl lemma pauliMatrix_contr_down_3_tree : {(basisVector ![Color.down, Color.down] fun x => 3) | μ ν ⊗ - PauliMatrix.asConsTensor | μ α β}ᵀ.tensor = + PauliMatrix.asConsTensor | μ α β}ᵀ.tensor = (TensorTree.add ((tensorNode (basisVector pauliMatrixLowerMap (fun | 0 => 3 | 1 => 0 | 2 => 0)))) (smul (-1) (tensorNode (basisVector pauliMatrixLowerMap diff --git a/HepLean/Tensors/Tree/NodeIdentities/Basic.lean b/HepLean/Tensors/Tree/NodeIdentities/Basic.lean index dbe3ec7..2553c16 100644 --- a/HepLean/Tensors/Tree/NodeIdentities/Basic.lean +++ b/HepLean/Tensors/Tree/NodeIdentities/Basic.lean @@ -203,7 +203,7 @@ lemma smul_prod {n m: ℕ} {c : Fin n → S.C} {c1 : Fin m → S.C} simp [prod_tensor, smul_tensor, tmul_smul, smul_tmul, map_smul] lemma prod_smul {n m : ℕ} {c : Fin n → S.C} {c1 : Fin m → S.C} - (a : S.k) (t1 : TensorTree S c) (t2 : TensorTree S c1) : + (a : S.k) (t1 : TensorTree S c) (t2 : TensorTree S c1) : (prod t1 (smul a t2)).tensor = (smul a (prod t1 t2)).tensor := by simp [prod_tensor, smul_tensor, tmul_smul, smul_tmul, map_smul]