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feat: Make MulActionTensor

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jstoobysmith 2024-07-30 07:51:07 -04:00
parent 99f4e85839
commit a65fb06605
11 changed files with 177 additions and 55 deletions
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7
HepLean/SpaceTime/LorentzTensor/Basic.lean
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@ -46,6 +46,7 @@ def contrDualMidAux {V1 V2 V3 V4 : Type} [AddCommMonoid V1] [AddCommMonoid V2] [
(V4 ⊗[R] V1) ⊗[R] (V2 ⊗[R] V3) →ₗ[R] V4 ⊗[R] V3 :=
(TensorProduct.map (LinearEquiv.refl R V4).toLinearMap (contrDualLeftAux f)) ∘ₗ
(TensorProduct.assoc R _ _ _).toLinearMap
/-- An initial structure specifying a tensor system (e.g. a system in which you can
define real Lorentz tensors or Einstein notation convention). -/
structure TensorStructure (R : Type) [CommSemiring R] where
@ -72,9 +73,9 @@ structure TensorStructure (R : Type) [CommSemiring R] where
/-- The unit is a right identity. -/
unit_lid : ∀ μ (x : ColorModule μ),
TensorProduct.rid R _
(TensorProduct.map (LinearEquiv.refl R (ColorModule μ)).toLinearMap
(contrDual μ ∘ₗ (TensorProduct.comm R _ _).toLinearMap )
((TensorProduct.assoc R _ _ _) (unit μ ⊗ₜ[R] x ))) = x
(TensorProduct.map (LinearEquiv.refl R (ColorModule μ)).toLinearMap
(contrDual μ ∘ₗ (TensorProduct.comm R _ _).toLinearMap)
((TensorProduct.assoc R _ _ _) (unit μ ⊗ₜ[R] x))) = x
/-- The metric for a given color. -/
metric : (μ : Color) → ColorModule μ ⊗[R] ColorModule μ
/-- The metric contracted with its dual is the unit. -/