2024-04-18 10:50:21 -04:00
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/-
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Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
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Released under Apache 2.0 license.
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Authors: Joseph Tooby-Smith
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-/
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2024-06-25 07:06:32 -04:00
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import HepLean.AnomalyCancellation.PureU1.Basic
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2024-04-18 10:50:21 -04:00
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/-!
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# The Pure U(1) case with 1 fermion
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We show that in this case the charge must be zero.
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-/
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universe v u
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open Nat
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open Finset
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namespace PureU1
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variable {n : ℕ}
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namespace One
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theorem solEqZero (S : (PureU1 1).LinSols) : S = 0 := by
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apply ACCSystemLinear.LinSols.ext
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have hLin := pureU1_linear S
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simp at hLin
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funext i
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simp at i
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2024-06-13 16:49:01 -04:00
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rw [show i = (0 : Fin 1) from Fin.fin_one_eq_zero i]
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2024-04-18 10:50:21 -04:00
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exact hLin
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end One
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end PureU1
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