Of Clifford Algebra ι single
spaceTime.γ.ofCliffordAlgebra_ι_single
Plain-language statement
The generators of the clifford algebra correspond to the elements γ.
Exact Lean statement
@[simp]
lemma ofCliffordAlgebra_ι_single (i : Fin 4) (r : ℝ) :
ofCliffordAlgebra (CliffordAlgebra.ι _ (Pi.single i r)) = r • ⟨γ i, γ_in_diracAlgebra _⟩Formal artifact
Lean source
@[simp]lemma ofCliffordAlgebra_ι_single (i : Fin 4) (r : ℝ) : ofCliffordAlgebra (CliffordAlgebra.ι _ (Pi.single i r)) = r • ⟨γ i, γ_in_diracAlgebra _⟩ := CliffordAlgebra.lift_ι_apply _ _ _ |>.trans <| Subtype.ext <| by simp only [γ, LinearMap.coe_sum, LinearMap.coe_smulRight, LinearMap.coe_proj, Function.eval, SetLike.mk_smul_mk, Finset.sum_apply, AddSubmonoidClass.coe_finsetSum] rw [Finset.sum_eq_single i] · simp · intro b _ hb simp [Pi.single_eq_of_ne hb] · simp- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Relativity/CliffordAlgebra.lean:131-141
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