2024-10-30 06:41:03 +00:00
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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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2024-11-09 17:46:52 +00:00
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import HepLean.Lorentz.ComplexTensor.Metrics.Basis
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import HepLean.Lorentz.ComplexTensor.Units.Basic
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import HepLean.Lorentz.ComplexTensor.Basis
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2024-10-30 06:41:03 +00:00
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/-!
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## Symmetry lemmas relating to units
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-/
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open IndexNotation
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open CategoryTheory
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open MonoidalCategory
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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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open IndexNotation
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open CategoryTheory
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open TensorTree
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open OverColor.Discrete
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noncomputable section
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namespace complexLorentzTensor
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/-!
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## Symmetry properties
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-/
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informal_lemma coContrUnit_symm where
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math :≈ "Swapping indices of coContrUnit returns contrCoUnit, i.e. {δ' | μ ν = δ | ν μ}.ᵀ"
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deps :≈ [``coContrUnit, ``contrCoUnit]
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informal_lemma contrCoUnit_symm where
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math :≈ "Swapping indices of contrCoUnit returns coContrUnit, i.e. {δ | μ ν = δ' | ν μ}ᵀ"
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deps :≈ [``contrCoUnit, ``coContrUnit]
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informal_lemma altLeftLeftUnit_symm where
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math :≈ "Swapping indices of altLeftLeftUnit returns leftAltLeftUnit, i.e.
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{δL' | α α' = δL | α' α}ᵀ"
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deps :≈ [``altLeftLeftUnit, ``leftAltLeftUnit]
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informal_lemma leftAltLeftUnit_symm where
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math :≈ "Swapping indices of leftAltLeftUnit returns altLeftLeftUnit, i.e.
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{δL | α α' = δL' | α' α}ᵀ"
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deps :≈ [``leftAltLeftUnit, ``altLeftLeftUnit]
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informal_lemma altRightRightUnit_symm where
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math :≈ "Swapping indices of altRightRightUnit returns rightAltRightUnit, i.e.
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{δR' | β β' = δR | β' β}ᵀ"
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deps :≈ [``altRightRightUnit, ``rightAltRightUnit]
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informal_lemma rightAltRightUnit_symm where
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math :≈ "Swapping indices of rightAltRightUnit returns altRightRightUnit, i.e.
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{δR | β β' = δR' | β' β}ᵀ"
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deps :≈ [``rightAltRightUnit, ``altRightRightUnit]
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end complexLorentzTensor
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