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

13
HepLean/SpaceTime/LorentzTensor/Real/Basic.lean
View file

@ -81,12 +81,12 @@ def realLorentzTensor (d : ℕ) : TensorStructure ℝ where
| .down => LorentzVector.unitDown_rid
metric μ :=
match μ with
| realTensor.ColorType.up => asProdLorentzVector
| realTensor.ColorType.down => asProdCovariantLorentzVector
| realTensor.ColorType.up => asTenProd
| realTensor.ColorType.down => asCoTenProd
metric_dual μ :=
match μ with
| realTensor.ColorType.up => asProdLorentzVector_contr_asCovariantProdLorentzVector
| realTensor.ColorType.down => asProdCovariantLorentzVector_contr_asProdLorentzVector
| realTensor.ColorType.up => asTenProd_contr_asCoTenProd
| realTensor.ColorType.down => asCoTenProd_contr_asTenProd
/-- The action of the Lorentz group on real Lorentz tensors. -/
instance : MulActionTensor (LorentzGroup d) (realLorentzTensor d) where
@ -98,5 +98,8 @@ instance : MulActionTensor (LorentzGroup d) (realLorentzTensor d) where
match μ with
| .up => TensorProduct.ext' (fun _ _ => LorentzVector.contrUpDown_invariant_lorentzAction)
| .down => TensorProduct.ext' (fun _ _ => LorentzVector.contrDownUp_invariant_lorentzAction)
metric_inv μ g :=
match μ with
| .up => asTenProd_invariant g
| .down => asCoTenProd_invariant g
end