39 lines
1 KiB
Text
39 lines
1 KiB
Text
/-
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Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Joseph Tooby-Smith
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-/
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import Mathlib.Data.Complex.Exponential
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import Mathlib.Analysis.InnerProductSpace.PiL2
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import HepLean.SpaceTime.SL2C.Basic
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import HepLean.SpaceTime.LorentzVector.Modules
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import HepLean.Meta.Informal
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import Mathlib.RepresentationTheory.Rep
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import HepLean.Tensors.Basic
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/-!
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# Complex Lorentz vectors
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We define complex Lorentz vectors in 4d space-time as representations of SL(2, C).
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-/
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noncomputable section
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open Matrix
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open MatrixGroups
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open Complex
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open TensorProduct
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namespace Lorentz
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/-- The representation of `SL(2, ℂ)` on complex vectors corresponding to contravariant
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Lorentz vectors. -/
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def complexContr : Rep ℂ SL(2, ℂ) := Rep.of ContrℂModule.SL2CRep
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/-- The representation of `SL(2, ℂ)` on complex vectors corresponding to contravariant
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Lorentz vectors. -/
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def complexCo : Rep ℂ SL(2, ℂ) := Rep.of CoℂModule.SL2CRep
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end Lorentz
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end
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