46 lines
1.4 KiB
Text
46 lines
1.4 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.StandardModel.Basic
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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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/-- The gauge group of the Georgi-Glashow model, i.e., `SU(5)`. -/
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informal_definition GaugeGroupI where
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deps := []
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/-- The homomorphism of the Standard Model gauge group into the Georgi-Glashow gauge group, i.e.,
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the group homomorphism `SU(3) × SU(2) × U(1) → SU(5)` taking `(h, g, α)` to
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`blockdiag (α ^ 3 g, α ^ (-2) h)`.
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See page 34 of https://math.ucr.edu/home/baez/guts.pdf
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-/
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informal_definition inclSM where
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deps := [``GaugeGroupI, ``StandardModel.GaugeGroupI]
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/-- The kernel of the map `inclSM` is equal to the subgroup `StandardModel.gaugeGroupℤ₆SubGroup`.
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See page 34 of https://math.ucr.edu/home/baez/guts.pdf
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-/
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informal_lemma inclSM_ker where
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deps := [``inclSM, ``StandardModel.gaugeGroupℤ₆SubGroup]
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/-- The group embedding from `StandardModel.GaugeGroupℤ₆` to `GaugeGroupI` induced by `inclSM` by
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quotienting by the kernel `inclSM_ker`.
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-/
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informal_definition embedSMℤ₆ where
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deps := [``inclSM, ``StandardModel.GaugeGroupℤ₆, ``GaugeGroupI, ``inclSM_ker]
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end GeorgiGlashow
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