2024-04-18 08:59:48 -04:00
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/-
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Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
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2024-07-12 16:39:44 -04:00
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Released under Apache 2.0 license as described in the file LICENSE.
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2024-04-18 08:59:48 -04:00
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Authors: Joseph Tooby-Smith
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-/
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import HepLean.AnomalyCancellation.SMNu.Ordinary.Basic
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import HepLean.AnomalyCancellation.SMNu.FamilyMaps
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/-!
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# Family Maps for SM with RHN (no hypercharge)
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We give some propererties of the family maps for the SM with RHN, in particular, we
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define family universal maps in the case of `LinSols`, `QuadSols`, and `Sols`.
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-/
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universe v u
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namespace SMRHN
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namespace SM
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open SMνCharges
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open SMνACCs
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open BigOperators
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variable {n : ℕ}
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/-- The family universal maps on `LinSols`. -/
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def familyUniversalLinear (n : ℕ) :
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(SM 1).LinSols →ₗ[ℚ] (SM n).LinSols where
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toFun S := chargeToLinear (familyUniversal n S.val)
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(by rw [familyUniversal_accGrav, gravSol S, mul_zero])
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(by rw [familyUniversal_accSU2, SU2Sol S, mul_zero])
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(by rw [familyUniversal_accSU3, SU3Sol S, mul_zero])
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map_add' S T := by
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apply ACCSystemLinear.LinSols.ext
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exact (familyUniversal n).map_add' _ _
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map_smul' a S := by
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apply ACCSystemLinear.LinSols.ext
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exact (familyUniversal n).map_smul' _ _
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/-- The family universal maps on `QuadSols`. -/
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def familyUniversalQuad (n : ℕ) :
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(SM 1).QuadSols → (SM n).QuadSols := fun S =>
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chargeToQuad (familyUniversal n S.val)
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(by rw [familyUniversal_accGrav, gravSol S.1, mul_zero])
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(by rw [familyUniversal_accSU2, SU2Sol S.1, mul_zero])
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(by rw [familyUniversal_accSU3, SU3Sol S.1, mul_zero])
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/-- The family universal maps on `Sols`. -/
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def familyUniversalAF (n : ℕ) :
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(SM 1).Sols → (SM n).Sols := fun S =>
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chargeToAF (familyUniversal n S.val)
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(by rw [familyUniversal_accGrav, gravSol S.1.1, mul_zero])
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(by rw [familyUniversal_accSU2, SU2Sol S.1.1, mul_zero])
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(by rw [familyUniversal_accSU3, SU3Sol S.1.1, mul_zero])
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(by rw [familyUniversal_accCube, cubeSol S, mul_zero])
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end SM
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end SMRHN
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