35 lines
1.2 KiB
Text
35 lines
1.2 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 HepLean.BeyondTheStandardModel.TwoHDM.Basic
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/-!
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# Gauge orbits for the 2HDM
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The main reference for material in this section is https://arxiv.org/pdf/hep-ph/0605184.
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-/
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namespace TwoHDM
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informal_definition prodMatrix where
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math :≈ "For two Higgs fields `Φ₁` and `Φ₂`, the map from space time to 2 x 2 complex matrices
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defined by ((Φ₁^†Φ₁, Φ₂^†Φ₁), (Φ₁^†Φ₂, Φ₂^†Φ₂)). "
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ref :≈ "https://arxiv.org/pdf/hep-ph/0605184 eq 3.8."
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deps :≈ [``StandardModel.HiggsVec, ``SpaceTime]
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informal_lemma prodMatrix_positive_semidefinite where
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math :≈ "For all x in ``SpaceTime, ``prodMatrix at `x` is positive semidefinite."
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deps :≈ [``prodMatrix, ``SpaceTime]
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informal_lemma prodMatrix_hermitian where
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math :≈ "For all x in ``SpaceTime, ``prodMatrix at `x` is hermitian."
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deps :≈ [``prodMatrix, ``SpaceTime]
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informal_lemma prodMatrix_smooth where
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math :≈ "The map ``prodMatrix is a smooth function on spacetime."
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deps :≈ [``prodMatrix]
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end TwoHDM
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