f8f94979ab
* make informal_definition and informal_lemma commands * drop the fields "math", "physics", and "proof" from InformalDefinition/InformalLemma and use docstrings instead * render informal docstring in dependency graph
57 lines
2.1 KiB
Text
57 lines
2.1 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.PatiSalam.Basic
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import HepLean.BeyondTheStandardModel.GeorgiGlashow.Basic
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/-!
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# The Spin(10) Model
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Note: By physicists this is usually called SO(10). However, the true gauge group involved
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is Spin(10).
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-/
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namespace Spin10Model
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/-- The gauge group of the Spin(10) model, i.e., the group `Spin(10)`. -/
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informal_definition GaugeGroupI where
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deps := []
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/-- The inclusion of the Pati-Salam gauge group into Spin(10), i.e., the lift of the embedding
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`SO(6) × SO(4) → SO(10)` to universal covers, giving a homomorphism `Spin(6) × Spin(4) → Spin(10)`.
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Precomposed with the isomorphism, `PatiSalam.gaugeGroupISpinEquiv`, between `SU(4) × SU(2) × SU(2)`
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and `Spin(6) × Spin(4)`.
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See page 56 of https://math.ucr.edu/home/baez/guts.pdf
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-/
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informal_definition inclPatiSalam where
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deps := [``GaugeGroupI, ``PatiSalam.GaugeGroupI, ``PatiSalam.gaugeGroupISpinEquiv]
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/-- The inclusion of the Standard Model gauge group into Spin(10), i.e., the compoisiton of
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`embedPatiSalam` and `PatiSalam.inclSM`.
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See page 56 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 := [``inclPatiSalam, ``PatiSalam.inclSM]
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/-- The inclusion of the Georgi-Glashow gauge group into Spin(10), i.e., the Lie group homomorphism
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from `SU(n) → Spin(2n)` discussed on page 46 of https://math.ucr.edu/home/baez/guts.pdf for `n = 5`.
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-/
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informal_definition inclGeorgiGlashow where
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deps := [``GaugeGroupI, ``GeorgiGlashow.GaugeGroupI]
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/-- The inclusion of the Standard Model gauge group into Spin(10), i.e., the composition of
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`inclGeorgiGlashow` and `GeorgiGlashow.inclSM`.
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-/
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informal_definition inclSMThruGeorgiGlashow where
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deps := [``inclGeorgiGlashow, ``GeorgiGlashow.inclSM]
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/-- The inclusion `inclSM` is equal to the inclusion `inclSMThruGeorgiGlashow`. -/
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informal_lemma inclSM_eq_inclSMThruGeorgiGlashow where
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deps := [``inclSM, ``inclSMThruGeorgiGlashow]
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end Spin10Model
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