DibyashanuPati/PhysLean
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

docs: Documentation related to Pauli-matrices

Browse source
This commit is contained in:
jstoobysmith 2024-11-26 11:38:22 +00:00
parent 3b5fbc27e3
commit 6db6752077
2 changed files with 29 additions and 3 deletions
Download patch file Download diff file Expand all files Collapse all files

2
HepLean/Lorentz/PauliMatrices/AsTensor.lean
View file

@ -189,6 +189,8 @@ def asConsTensor : 𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ complexContr ⊗ leftHanded ⊗
CategoryTheory.Equivalence.symm_inverse, Action.functorCategoryEquivalence_functor,
Action.FunctorCategoryEquivalence.functor_obj_obj]
/-- The map `𝟙_ (Rep ℂ SL(2,ℂ)) ⟶ complexContr ⊗ leftHanded ⊗ rightHanded` corresponding
to Pauli matrices, when evaluated on `1` corresponds to the tensor `PauliMatrix.asTensor`. -/
lemma asConsTensor_apply_one : asConsTensor.hom (1 : ℂ) = asTensor := by
change asConsTensor.hom.toFun (1 : ℂ) = asTensor
simp only [Action.instMonoidalCategory_tensorObj_V, Action.instMonoidalCategory_tensorUnit_V,