Repr conj Chiral Covector
SUSY.N1.repr_conjChiralCovector
Plain-language statement
Component formula for the holomorphic covector conjugate: the ![I] basis component of conjChiralCovector t is the complex conjugate of the ![I] component of t.
Exact Lean statement
lemma repr_conjChiralCovector
(t : (chiralTensor (ι := ι)).Tensor ![chiralDown]) (I : ι) :
(basis (S := (chiralTensor (ι := ι)).toTensorSpecies) ![antiDown]).repr
(conjChiralCovector t) ![I] =
star ((basis (S := (chiralTensor (ι := ι)).toTensorSpecies) ![chiralDown]).repr t ![I])Formal artifact
Lean source
lemma repr_conjChiralCovector (t : (chiralTensor (ι := ι)).Tensor ![chiralDown]) (I : ι) : (basis (S := (chiralTensor (ι := ι)).toTensorSpecies) ![antiDown]).repr (conjChiralCovector t) ![I] = star ((basis (S := (chiralTensor (ι := ι)).toTensorSpecies) ![chiralDown]).repr t ![I]) := by rw [conjChiralCovector, permT_basis_repr_symm_apply] change componentMap (S := (chiralTensor (ι := ι)).toTensorSpecies) ((chiralTensor (ι := ι)).bar ∘ ![chiralDown]) ((chiralTensor (ι := ι)).conjT t) _ = _ erw [ConjTensorSpecies.componentMap_conjT (S := chiralTensor (ι := ι))] apply congrArg star apply congrArg (fun idx => componentMap (S := (chiralTensor (ι := ι)).toTensorSpecies) ![chiralDown] t idx) funext i fin_cases i rfl- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Particles/SuperSymmetry/N1/Basic.lean:427-441
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