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

docs: CKM Relations

Browse source
This commit is contained in:
jstoobysmith 2024-11-27 06:38:31 +00:00
parent 3e2a801c70
commit e9ce319101
4 changed files with 25 additions and 3 deletions
Download patch file Download diff file Expand all files Collapse all files

6
HepLean/Lorentz/ComplexTensor/Basis.lean
View file

@ -63,6 +63,7 @@ lemma basis_eq_FD {n : ℕ} (c : Fin n → complexLorentzTensor.C)
subst h'
rfl
/-- The `perm` node acting on basis vectors corresponds to a basis vector. -/
lemma perm_basisVector {n m : ℕ} {c : Fin n → complexLorentzTensor.C}
{c1 : Fin m → complexLorentzTensor.C} (σ : OverColor.mk c ⟶ OverColor.mk c1)
(b : Π j, Fin (complexLorentzTensor.repDim (c j))) :
@ -79,6 +80,8 @@ lemma perm_basisVector {n m : ℕ} {c : Fin n → complexLorentzTensor.C}
eqToIso.hom, Functor.mapIso_inv, eqToIso.inv, LinearEquiv.ofLinear_apply]
rw [basis_eq_FD]
/-- The `perm` node acting on basis vectors corresponds to a basis vector, as a tensor tree
structue. -/
lemma perm_basisVector_tree {n m : ℕ} {c : Fin n → complexLorentzTensor.C}
{c1 : Fin m → complexLorentzTensor.C} (σ : OverColor.mk c ⟶ OverColor.mk c1)
(b : Π j, Fin (complexLorentzTensor.repDim (c j))) :
@ -168,6 +171,7 @@ def prodBasisVecEquiv {n m : ℕ} {c : Fin n → complexLorentzTensor.C}
| Sum.inl _ => Equiv.refl _
| Sum.inr _ => Equiv.refl _
/-- The `prod` node acting on basis vectors corresponds to a basis vector. -/
lemma prod_basisVector {n m : ℕ} {c : Fin n → complexLorentzTensor.C}
{c1 : Fin m → complexLorentzTensor.C}
(b : Π k, Fin (complexLorentzTensor.repDim (c k)))
@ -197,6 +201,7 @@ lemma prod_basisVector {n m : ℕ} {c : Fin n → complexLorentzTensor.C}
| Sum.inl k => rfl
| Sum.inr k => rfl
/-- The prod node acting on a basis vectors is a basis vector, as a tensor tree structure. -/
lemma prod_basisVector_tree {n m : ℕ} {c : Fin n → complexLorentzTensor.C}
{c1 : Fin m → complexLorentzTensor.C}
(b : Π k, Fin (complexLorentzTensor.repDim (c k)))
@ -207,6 +212,7 @@ lemma prod_basisVector_tree {n m : ℕ} {c : Fin n → complexLorentzTensor.C}
((HepLean.PiTensorProduct.elimPureTensor b b1) (finSumFinEquiv.symm i))))).tensor := by
exact prod_basisVector _ _
/-- The `eval` node acting on basis vectors corresponds to a basis vector. -/
lemma eval_basisVector {n : ℕ} {c : Fin n.succ → complexLorentzTensor.C}
{i : Fin n.succ} (j : Fin (complexLorentzTensor.repDim (c i)))
(b : Π k, Fin (complexLorentzTensor.repDim (c k))) :