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

feat: Add metric invariance for Real Lorentz Tensors

Browse source
This commit is contained in:
jstoobysmith 2024-07-31 08:52:09 -04:00
parent 8b2c853fd8
commit 7b0b979d51
7 changed files with 175 additions and 24 deletions
Download patch file Download diff file Expand all files Collapse all files

10
HepLean/SpaceTime/LorentzVector/Covariant.lean
View file

@ -94,6 +94,16 @@ lemma rep_apply (g : LorentzGroup d) : rep g v = (g.1⁻¹)ᵀ *ᵥ v := by
rw [← LorentzGroup.coe_inv]
rfl
lemma rep_apply_stdBasis (g : LorentzGroup d) (μ : Fin 1 ⊕ Fin d) :
rep g (stdBasis μ) = ∑ ν, g⁻¹.1 μ ν • stdBasis ν := by
simp only [rep_apply, Fintype.sum_sum_type, Finset.univ_unique, Fin.default_eq_zero, Fin.isValue,
Finset.sum_singleton, decomp_stdBasis']
funext ν
simp [LorentzVector.stdBasis, Pi.basisFun_apply]
erw [Pi.basisFun_apply, Matrix.mulVec_stdBasis]
rw [← LorentzGroup.coe_inv]
simp
end CovariantLorentzVector
end