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

feat: Add eval basis for complex Lorentz tensors

Browse source
This commit is contained in:
jstoobysmith 2024-10-21 16:21:29 +00:00
parent 920ced9449
commit 4007f1a463
2 changed files with 17 additions and 1 deletions
Download patch file Download diff file Expand all files Collapse all files

8
HepLean/SpaceTime/LorentzVector/Complex/Basic.lean
View file

@ -40,6 +40,10 @@ def complexCo : Rep ℂ SL(2, ℂ) := Rep.of CoℂModule.SL2CRep
def complexContrBasis : Basis (Fin 1 ⊕ Fin 3) ℂ complexContr := Basis.ofEquivFun
(Equiv.linearEquiv ℂ ContrℂModule.toFin13ℂFun)
/-- The standard basis of complex contravariant Lorentz vectors indexed by `Fin 4`. -/
def complexContrBasisFin4 : Basis (Fin 4) ℂ complexContr :=
Basis.reindex complexContrBasis finSumFinEquiv
@[simp]
lemma complexContrBasis_ρ_apply (M : SL(2,ℂ)) (i j : Fin 1 ⊕ Fin 3) :
(LinearMap.toMatrix complexContrBasis complexContrBasis) (complexContr.ρ M) i j =
@ -58,6 +62,10 @@ lemma complexContrBasis_ρ_val (M : SL(2,ℂ)) (v : complexContr) :
def complexCoBasis : Basis (Fin 1 ⊕ Fin 3) ℂ complexCo := Basis.ofEquivFun
(Equiv.linearEquiv ℂ CoℂModule.toFin13ℂFun)
/-- The standard basis of complex covariant Lorentz vectors indexed by `Fin 4`. -/
def complexCoBasisFin4 : Basis (Fin 4) ℂ complexCo :=
Basis.reindex complexCoBasis finSumFinEquiv
@[simp]
lemma complexCoBasis_ρ_apply (M : SL(2,ℂ)) (i j : Fin 1 ⊕ Fin 3) :
(LinearMap.toMatrix complexCoBasis complexCoBasis) (complexCo.ρ M) i j =