2024-09-24 08:55:30 +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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import HepLean.StandardModel.Basic
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2024-12-05 06:49:50 +00:00
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import HepLean.Meta.Informal.Basic
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2024-09-24 08:55:30 +00:00
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/-!
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# The Georgi-Glashow Model
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The Georgi-Glashow model is a grand unified theory that unifies the Standard Model gauge group into
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`SU(5)`.
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This file currently contains informal-results about the Georgi-Glashow group.
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-/
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namespace GeorgiGlashow
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informal_definition GaugeGroupI where
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math :≈ "The group `SU(5)`."
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physics :≈ "The gauge group of the Georgi-Glashow model."
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informal_definition inclSM where
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physics :≈ "The homomorphism of the Standard Model gauge group into the
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Georgi-Glashow gauge group."
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math :≈ "The group homomorphism `SU(3) x SU(2) x U(1) -> SU(5)`
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taking (h, g, α) to (blockdiag (α ^ 3 g, α ^ (-2) h)."
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ref :≈ "Page 34 of https://math.ucr.edu/home/baez/guts.pdf"
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deps :≈ [``GaugeGroupI, ``StandardModel.GaugeGroupI]
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informal_lemma inclSM_ker where
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math :≈ "The kernel of the map ``inclSM is equal to the subgroup
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``StandardModel.gaugeGroupℤ₆SubGroup."
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ref :≈ "Page 34 of https://math.ucr.edu/home/baez/guts.pdf"
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deps :≈ [``inclSM, ``StandardModel.gaugeGroupℤ₆SubGroup]
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informal_definition embedSMℤ₆ where
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math :≈ "The group embedding from ``StandardModel.GaugeGroupℤ₆ to ``GaugeGroupI
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induced by ``inclSM by quotienting by the kernal ``inclSM_ker."
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deps :≈ [``inclSM, ``StandardModel.GaugeGroupℤ₆, ``GaugeGroupI, ``inclSM_ker]
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end GeorgiGlashow
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