chore: bump to v4.16.0
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35 changed files with 200 additions and 145 deletions
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@ -84,8 +84,8 @@ TODO "Make `HiggsBundle` an associated bundle."
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abbrev HiggsBundle := Bundle.Trivial SpaceTime HiggsVec
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/-- The instance of a smooth vector bundle with total space `HiggsBundle` and fiber `HiggsVec`. -/
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instance : SmoothVectorBundle HiggsVec HiggsBundle SpaceTime.asSmoothManifold :=
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Bundle.Trivial.smoothVectorBundle HiggsVec
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instance : ContMDiffVectorBundle ⊤ HiggsVec HiggsBundle SpaceTime.asSmoothManifold :=
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Bundle.Trivial.contMDiffVectorBundle HiggsVec
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/-- A Higgs field is a smooth section of the Higgs bundle. -/
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abbrev HiggsField : Type := ContMDiffSection SpaceTime.asSmoothManifold HiggsVec ⊤ HiggsBundle
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@ -210,10 +210,12 @@ theorem rotate_fst_real_snd_zero (φ : HiggsVec) :
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coe_smul, mulVec_empty, add_zero, zero_add, one_smul]
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funext i
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fin_cases i
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· simp only [Fin.zero_eta, Fin.isValue, Pi.smul_apply, Function.comp_apply, cons_val_zero,
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tail_cons, head_cons, real_smul, mul_one]
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· simp only [Fin.mk_one, Fin.isValue, Pi.smul_apply, Function.comp_apply, cons_val_one, head_cons,
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tail_cons, smul_zero]
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· simp only [one_pow, mulVec_cons, Nat.succ_eq_add_one, Nat.reduceAdd, zero_smul, coe_smul,
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mulVec_empty, add_zero, zero_add, Fin.zero_eta, Fin.isValue, Pi.smul_apply, Function.comp_apply,
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cons_val_zero, tail_cons, head_cons, real_smul, mul_one, one_smul, P]
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· simp only [one_pow, mulVec_cons, Nat.succ_eq_add_one, Nat.reduceAdd, zero_smul, coe_smul,
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mulVec_empty, add_zero, zero_add, Fin.mk_one, Fin.isValue, Pi.smul_apply, Function.comp_apply,
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cons_val_one, head_cons, tail_cons, smul_zero, P]
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/-- There exists a `g` in `GaugeGroupI` such that `rep g φ = φ'` iff `‖φ‖ = ‖φ'‖`. -/
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informal_lemma guage_orbit where
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