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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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70
HepLean/Tensors/Tree/Elab.lean
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@ -23,7 +23,7 @@ open Lean.Elab
open Lean.Elab.Term
open Lean Meta Elab Tactic
open IndexNotation
open complexLorentzTensor
namespace TensorTree
/-!
@ -182,60 +182,60 @@ def stringToTerm (str : String) : TermElabM Term := do
/-- Specific types of tensors which appear which we want to elaborate in specific ways. -/
def specialTypes : List (String × (Term → Term)) := [
("CoeSort.coe Lorentz.complexCo", fun T =>
Syntax.mkApp (mkIdent ``TensorTree.vecNodeE) #[mkIdent ``Fermion.complexLorentzTensor,
mkIdent ``Fermion.Color.down, T]),
Syntax.mkApp (mkIdent ``TensorTree.vecNodeE) #[mkIdent ``complexLorentzTensor,
mkIdent ``complexLorentzTensor.Color.down, T]),
("CoeSort.coe Lorentz.complexContr", fun T =>
Syntax.mkApp (mkIdent ``TensorTree.vecNodeE) #[mkIdent ``Fermion.complexLorentzTensor,
mkIdent ``Fermion.Color.up, T]),
Syntax.mkApp (mkIdent ``TensorTree.vecNodeE) #[mkIdent ``complexLorentzTensor,
mkIdent ``complexLorentzTensor.Color.up, T]),
("ModuleCat.carrier (Lorentz.complexContr ⊗ Lorentz.complexCo).V", fun T =>
Syntax.mkApp (mkIdent ``TensorTree.twoNodeE) #[mkIdent ``Fermion.complexLorentzTensor,
mkIdent ``Fermion.Color.up, mkIdent ``Fermion.Color.down, T]),
Syntax.mkApp (mkIdent ``TensorTree.twoNodeE) #[mkIdent ``complexLorentzTensor,
mkIdent ``complexLorentzTensor.Color.up, mkIdent ``complexLorentzTensor.Color.down, T]),
("ModuleCat.carrier (Lorentz.complexContr ⊗ Lorentz.complexContr).V", fun T =>
Syntax.mkApp (mkIdent ``TensorTree.twoNodeE) #[mkIdent ``Fermion.complexLorentzTensor,
mkIdent ``Fermion.Color.up, mkIdent ``Fermion.Color.up, T]),
Syntax.mkApp (mkIdent ``TensorTree.twoNodeE) #[mkIdent ``complexLorentzTensor,
mkIdent ``complexLorentzTensor.Color.up, mkIdent ``complexLorentzTensor.Color.up, T]),
("ModuleCat.carrier (Lorentz.complexCo ⊗ Lorentz.complexCo).V", fun T =>
Syntax.mkApp (mkIdent ``TensorTree.twoNodeE) #[mkIdent ``Fermion.complexLorentzTensor,
mkIdent ``Fermion.Color.down, mkIdent ``Fermion.Color.down, T]),
Syntax.mkApp (mkIdent ``TensorTree.twoNodeE) #[mkIdent ``complexLorentzTensor,
mkIdent ``complexLorentzTensor.Color.down, mkIdent ``complexLorentzTensor.Color.down, T]),
("ModuleCat.carrier (Lorentz.complexCo ⊗ Lorentz.complexContr).V", fun T =>
Syntax.mkApp (mkIdent ``TensorTree.twoNodeE) #[
mkIdent ``Fermion.complexLorentzTensor,
mkIdent ``Fermion.Color.down,
mkIdent ``Fermion.Color.up, T]),
mkIdent ``complexLorentzTensor,
mkIdent ``complexLorentzTensor.Color.down,
mkIdent ``complexLorentzTensor.Color.up, T]),
("𝟙_ (Rep ℂ SL(2, ℂ)) ⟶ Lorentz.complexCo ⊗ Lorentz.complexCo", fun T =>
Syntax.mkApp (mkIdent ``TensorTree.constTwoNodeE) #[
mkIdent ``Fermion.complexLorentzTensor,
mkIdent ``Fermion.Color.down,
mkIdent ``Fermion.Color.down, T]),
mkIdent ``complexLorentzTensor,
mkIdent ``complexLorentzTensor.Color.down,
mkIdent ``complexLorentzTensor.Color.down, T]),
("𝟙_ (Rep ℂ SL(2, ℂ)) ⟶ Lorentz.complexContr ⊗ Lorentz.complexContr", fun T =>
Syntax.mkApp (mkIdent ``TensorTree.constTwoNodeE) #[
mkIdent ``Fermion.complexLorentzTensor,
mkIdent ``Fermion.Color.up,
mkIdent ``Fermion.Color.up, T]),
mkIdent ``complexLorentzTensor,
mkIdent ``complexLorentzTensor.Color.up,
mkIdent ``complexLorentzTensor.Color.up, T]),
("𝟙_ (Rep ℂ SL(2, ℂ)) ⟶ Lorentz.complexContr ⊗ Fermion.leftHanded ⊗ Fermion.rightHanded", fun T =>
Syntax.mkApp (mkIdent ``TensorTree.constThreeNodeE) #[
mkIdent ``Fermion.complexLorentzTensor, mkIdent ``Fermion.Color.up,
mkIdent ``Fermion.Color.upL,
mkIdent ``Fermion.Color.upR, T]),
mkIdent ``complexLorentzTensor, mkIdent ``complexLorentzTensor.Color.up,
mkIdent ``complexLorentzTensor.Color.upL,
mkIdent ``complexLorentzTensor.Color.upR, T]),
("𝟙_ (Rep ℂ SL(2, ℂ)) ⟶ Fermion.leftHanded ⊗ Fermion.leftHanded", fun T =>
Syntax.mkApp (mkIdent ``TensorTree.constTwoNodeE) #[
mkIdent ``Fermion.complexLorentzTensor,
mkIdent ``Fermion.Color.upL,
mkIdent ``Fermion.Color.upL, T]),
mkIdent ``complexLorentzTensor,
mkIdent ``complexLorentzTensor.Color.upL,
mkIdent ``complexLorentzTensor.Color.upL, T]),
("𝟙_ (Rep ℂ SL(2, ℂ)) ⟶ Fermion.altLeftHanded ⊗ Fermion.altLeftHanded", fun T =>
Syntax.mkApp (mkIdent ``TensorTree.constTwoNodeE) #[
mkIdent ``Fermion.complexLorentzTensor,
mkIdent ``Fermion.Color.downL,
mkIdent ``Fermion.Color.downL, T]),
mkIdent ``complexLorentzTensor,
mkIdent ``complexLorentzTensor.Color.downL,
mkIdent ``complexLorentzTensor.Color.downL, T]),
("𝟙_ (Rep ℂ SL(2, ℂ)) ⟶ Fermion.altRightHanded ⊗ Fermion.altRightHanded", fun T =>
Syntax.mkApp (mkIdent ``TensorTree.constTwoNodeE) #[
mkIdent ``Fermion.complexLorentzTensor,
mkIdent ``Fermion.Color.downR,
mkIdent ``Fermion.Color.downR, T]),
mkIdent ``complexLorentzTensor,
mkIdent ``complexLorentzTensor.Color.downR,
mkIdent ``complexLorentzTensor.Color.downR, T]),
("𝟙_ (Rep ℂ SL(2, ℂ)) ⟶ Fermion.rightHanded ⊗ Fermion.rightHanded", fun T =>
Syntax.mkApp (mkIdent ``TensorTree.constTwoNodeE) #[
mkIdent ``Fermion.complexLorentzTensor,
mkIdent ``Fermion.Color.upR,
mkIdent ``Fermion.Color.upR, T])]
mkIdent ``complexLorentzTensor,
mkIdent ``complexLorentzTensor.Color.upR,
mkIdent ``complexLorentzTensor.Color.upR, T])]
/-- The syntax associated with a terminal node of a tensor tree. -/
def termNodeSyntax (T : Term) : TermElabM Term := do