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refactor: Replace FDiscrete with FD

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jstoobysmith 2024-11-05 14:37:10 +00:00
parent bfaaf36485
commit 5acf22c479
9 changed files with 223 additions and 223 deletions
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2
HepLean/Tensors/ComplexLorentz/Basic.lean
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@ -88,7 +88,7 @@ def complexLorentzTensor : TensorSpecies where
G_group := inferInstance
k := ℂ
k_commRing := inferInstance
FDiscrete := Discrete.functor fun c =>
FD := Discrete.functor fun c =>
match c with
| Color.upL => Fermion.leftHanded
| Color.downL => Fermion.altLeftHanded

12
HepLean/Tensors/ComplexLorentz/Basis.lean
View file

@ -51,11 +51,11 @@ lemma perm_basisVector_cast {n m : ℕ} {c : Fin n → complexLorentzTensor.C}
simp only [Functor.const_obj_obj, OverColor.mk_hom] at h1
rw [h1]
/-! TODO: Generalize `basis_eq_FDiscrete`. -/
lemma basis_eq_FDiscrete {n : ℕ} (c : Fin n → complexLorentzTensor.C)
/-! TODO: Generalize `basis_eq_FD`. -/
lemma basis_eq_FD {n : ℕ} (c : Fin n → complexLorentzTensor.C)
(b : Π j, Fin (complexLorentzTensor.repDim (c j))) (i : Fin n)
(h : { as := c i } = { as := c1 }) :
(complexLorentzTensor.FDiscrete.map (eqToHom h)).hom
(complexLorentzTensor.FD.map (eqToHom h)).hom
(complexLorentzTensor.basis (c i) (b i)) =
(complexLorentzTensor.basis c1 (Fin.cast (by simp_all) (b i))) := by
have h' : c i = c1 := by
@ -77,7 +77,7 @@ lemma perm_basisVector {n m : ℕ} {c : Fin n → complexLorentzTensor.C}
funext i
simp only [OverColor.mk_hom, OverColor.lift.discreteFunctorMapEqIso, Functor.mapIso_hom,
eqToIso.hom, Functor.mapIso_inv, eqToIso.inv, LinearEquiv.ofLinear_apply]
rw [basis_eq_FDiscrete]
rw [basis_eq_FD]
lemma perm_basisVector_tree {n m : ℕ} {c : Fin n → complexLorentzTensor.C}
{c1 : Fin m → complexLorentzTensor.C} (σ : OverColor.mk c ⟶ OverColor.mk c1)
@ -120,7 +120,7 @@ lemma contr_basisVector {n : ℕ} {c : Fin n.succ.succ → complexLorentzTensor.
rw [basisVector]
erw [TensorSpecies.contrMap_tprod]
congr 1
rw [basis_eq_FDiscrete]
rw [basis_eq_FD]
simp only [Monoidal.tensorUnit_obj, Action.instMonoidalCategory_tensorUnit_V,
Equivalence.symm_inverse, Action.functorCategoryEquivalence_functor,
Action.FunctorCategoryEquivalence.functor_obj_obj, Functor.comp_obj, Discrete.functor_obj_eq_as,
@ -181,7 +181,7 @@ lemma prod_basisVector {n m : ℕ} {c : Fin n → complexLorentzTensor.C}
Action.instMonoidalCategory_tensorObj_V, Equivalence.symm_inverse,
Action.functorCategoryEquivalence_functor, Action.FunctorCategoryEquivalence.functor_obj_obj,
tensorNode_tensor]
have h1 := OverColor.lift.μ_tmul_tprod_mk complexLorentzTensor.FDiscrete
have h1 := OverColor.lift.μ_tmul_tprod_mk complexLorentzTensor.FD
(fun i => (complexLorentzTensor.basis (c i)) (b i))
(fun i => (complexLorentzTensor.basis (c1 i)) (b1 i))
erw [h1, OverColor.lift.map_tprod]