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feat: Add real lorentz tensors

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jstoobysmith 2024-07-29 16:54:59 -04:00
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commit 99f4e85839
13 changed files with 602 additions and 48 deletions
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HepLean/SpaceTime/LorentzTensor/RisingLowering.lean
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/-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
import HepLean.SpaceTime.LorentzTensor.Contractions
/-!
# Structure for Rising and Lowering indices
-/
noncomputable section
open TensorProduct
variable {R : Type} [CommSemiring R]
/-- Structure extending `TensorStructure` with the addition of a metric
permitting to `rise` and `lower` indices. -/
structure DualizeTensorStructure (R : Type) [CommSemiring R] extends TensorStructure R where
/-- The metric for a given color. -/
metric : Color → ColorModule (τ μ) ⊗[R] ColorModule (τ μ)
/-- The metric contracted with its dual is the unit. -/
metric_dual : ∀ μ,
TensorProduct.congr (LinearEquiv.refl _ _) (toTensorStructure.colorModuleCast (τ_involutive μ))
(toTensorStructure.contrTwoTwo (metric μ ⊗ₜ[R] metric (τ μ))) = unit μ
end