refactor: lint
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5 changed files with 5 additions and 9 deletions
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@ -4,7 +4,6 @@ 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 PhysLean.Electromagnetism.Basic
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import PhysLean.Relativity.SpaceTime.Basic
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/-!
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# Maxwell's equations
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@ -4,10 +4,8 @@ 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 PhysLean.Relativity.SpaceTime.Basic
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import Mathlib.Tactic.Polyrith
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import Mathlib.Geometry.Manifold.VectorBundle.SmoothSection
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import Mathlib.Geometry.Manifold.Instances.Real
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import PhysLean.Meta.Informal.Basic
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/-!
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# The Higgs field
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@ -4,10 +4,8 @@ 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 PhysLean.Particles.StandardModel.HiggsBoson.Basic
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import Mathlib.RepresentationTheory.Basic
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import PhysLean.Particles.StandardModel.Basic
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import PhysLean.Particles.StandardModel.Representations
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import Mathlib.Analysis.InnerProductSpace.Adjoint
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/-!
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# The action of the gauge group on the Higgs field
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@ -82,9 +82,11 @@ lemma toCoord_tprod {d : ℕ} (p : (i : Fin 1) →
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((Lorentz.contrBasisFin d).repr (p 0))
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(indexEquiv.symm i 0) := by
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rw [toCoord_apply]
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simp
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simp only [Nat.succ_eq_add_one, Nat.reduceAdd, C_eq_color, OverColor.mk_left, Functor.id_obj,
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OverColor.mk_hom, Equiv.piCongrLeft'_apply, Finsupp.equivFunOnFinite_apply, Fin.isValue]
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erw [TensorSpecies.TensorBasis.tensorBasis_repr_tprod]
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simp
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simp only [Finset.univ_unique, Fin.default_eq_zero, Fin.isValue, C_eq_color,
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Finset.prod_singleton, cons_val_zero]
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rfl
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lemma tensorNode_repr_apply {d : ℕ} (p : Vector d)
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@ -294,7 +296,6 @@ lemma action_apply_eq_sum (i : Fin 1 ⊕ Fin d) (Λ : LorentzGroup d) (p : Vecto
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rw [← mul_assoc, mul_comm _ r, mul_assoc]
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rw [← Finset.mul_sum]
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congr
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have hl : (𝟭 Type).obj (OverColor.mk ![Color.up]).left = Fin 1 := by rfl
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simp_all only [Nat.succ_eq_add_one, OverColor.mk_left, _root_.zero_add, Functor.id_obj,
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C_eq_color, OverColor.mk_hom]
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erw [toCoord_tprod]
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@ -54,7 +54,7 @@ lemma contrBasisFin_toFin1dℝ {d : ℕ} (i : Fin (1 + d)) :
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simp only [contrBasisFin, Basis.reindex_apply, contrBasis_toFin1dℝ, Basis.coe_ofEquivFun]
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lemma contrBasisFin_repr_apply {d : ℕ} (p : Contr d) (i : Fin (1 + d)) :
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(contrBasisFin d).repr p i = p.val (finSumFinEquiv.symm i) := by rfl
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(contrBasisFin d).repr p i = p.val (finSumFinEquiv.symm i) := by rfl
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/-- The representation of contravariant Lorentz vectors forms a topological space, induced
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by its equivalence to `Fin 1 ⊕ Fin d → ℝ`. -/
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