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feat: Fix pauli matrices as tensors. Speedup

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jstoobysmith 2024-10-25 13:50:19 +00:00
parent c565e7ea1c
commit e6ef68d7e6
9 changed files with 692 additions and 322 deletions
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11
HepLean/Tensors/ComplexLorentz/Basis.lean
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@ -32,8 +32,8 @@ open IndexNotation
open CategoryTheory
open TensorTree
open OverColor.Discrete
open Fermion
noncomputable section
namespace Fermion
namespace complexLorentzTensor
/-- Basis vectors for complex Lorentz tensors. -/
@ -95,7 +95,7 @@ def contrBasisVectorMul {n : ℕ} {c : Fin n.succ.succ → complexLorentzTensor.
lemma contrBasisVectorMul_neg {n : ℕ} {c : Fin n.succ.succ → complexLorentzTensor.C}
{i : Fin n.succ.succ} {j : Fin n.succ} {b : Π k, Fin (complexLorentzTensor.repDim (c k))}
(h : ¬ (b i).val = (b (i.succAbove j)).val := by decide) :
(h : ¬ (b i).val = (b (i.succAbove j)).val) :
contrBasisVectorMul i j b = 0 := by
rw [contrBasisVectorMul]
simp only [ite_eq_else, one_ne_zero, imp_false]
@ -103,7 +103,7 @@ lemma contrBasisVectorMul_neg {n : ℕ} {c : Fin n.succ.succ → complexLorentzT
lemma contrBasisVectorMul_pos {n : ℕ} {c : Fin n.succ.succ → complexLorentzTensor.C}
{i : Fin n.succ.succ} {j : Fin n.succ} {b : Π k, Fin (complexLorentzTensor.repDim (c k))}
(h : (b i).val = (b (i.succAbove j)).val := by decide) :
(h : (b i).val = (b (i.succAbove j)).val) :
contrBasisVectorMul i j b = 1 := by
rw [contrBasisVectorMul]
simp only [ite_eq_then, zero_ne_one, imp_false, Decidable.not_not]
@ -156,7 +156,7 @@ lemma contr_basisVector_tree_neg {n : ℕ} {c : Fin n.succ.succ → complexLoren
(tensorNode 0).tensor := by
rw [contr_basisVector_tree, contrBasisVectorMul]
rw [if_neg hn]
simp only [Nat.succ_eq_add_one, smul_tensor, tensorNode_tensor, zero_smul]
simp only [Nat.succ_eq_add_one, smul_tensor, tensorNode_tensor, _root_.zero_smul]
/-- Equivalence of Fin types appearing in the product of two basis vectors. -/
def prodBasisVecEquiv {n m : ℕ} {c : Fin n → complexLorentzTensor.C}
@ -214,7 +214,7 @@ lemma eval_basisVector {n : ℕ} {c : Fin n.succ → complexLorentzTensor.C}
basisVector (c ∘ Fin.succAbove i) (fun k => b (i.succAbove k)) := by
rw [eval_tensor, basisVector, basisVector]
simp only [Nat.succ_eq_add_one, Functor.id_obj, OverColor.mk_hom, tensorNode_tensor,
Function.comp_apply, one_smul, zero_smul]
Function.comp_apply, one_smul, _root_.zero_smul]
erw [TensorSpecies.evalMap_tprod]
congr 1
have h1 : Fin.ofNat' ↑j (@Fin.size_pos' (complexLorentzTensor.repDim (c i)) _) = j := by
@ -448,5 +448,4 @@ lemma pauliMatrix_basis_expand_tree : {PauliMatrix.asConsTensor | μ α β}ᵀ.t
rfl
end complexLorentzTensor
end Fermion
end