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feat: Add contraction of metric property for complex

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jstoobysmith 2024-10-24 16:35:15 +00:00
parent 8c584431c4
commit 833a570ce8
4 changed files with 185 additions and 2 deletions
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9
HepLean/Tensors/ComplexLorentz/Basic.lean
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@ -183,7 +183,14 @@ def complexLorentzTensor : TensorSpecies where
| Color.downR => Fermion.rightAltRightUnit_symm
| Color.up => Lorentz.coContrUnit_symm
| Color.down => Lorentz.contrCoUnit_symm
contr_metric := by sorry
contr_metric := fun c =>
match c with
| Color.upL => by simpa using Fermion.leftAltContraction_apply_metric
| Color.downL => by simpa using Fermion.altLeftContraction_apply_metric
| Color.upR => by simpa using Fermion.rightAltContraction_apply_metric
| Color.downR => by simpa using Fermion.altRightContraction_apply_metric
| Color.up => by simpa using Lorentz.contrCoContraction_apply_metric
| Color.down => by simpa using Lorentz.coContrContraction_apply_metric
instance : DecidableEq complexLorentzTensor.C := Fermion.instDecidableEqColor