2024-06-11 11:16:31 -04:00
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/-
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Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
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Released under Apache 2.0 license.
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Authors: Joseph Tooby-Smith
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-/
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import HepLean.SpaceTime.LorentzAlgebra.Basic
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/-!
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# Basis of the Lorentz Algebra
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We define the standard basis of the Lorentz group.
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-/
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namespace spaceTime
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namespace lorentzAlgebra
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open Matrix
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2024-06-11 11:33:50 -04:00
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/-- The matrices which form the basis of the Lorentz algebra. -/
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2024-06-11 11:16:31 -04:00
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@[simp]
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def σMat (μ ν : Fin 4) : Matrix (Fin 4) (Fin 4) ℝ := fun ρ δ ↦
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η^[ρ]_[μ] * η_[ν]_[δ] - η_[μ]_[δ] * η^[ρ]_[ν]
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end lorentzAlgebra
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end spaceTime
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