Dist Tensor Deriv basis repr apply
Electromagnetism.DistElectromagneticPotential.distTensorDeriv_basis_repr_apply
Project documentation
The creation of an electromagnetic potential from a static vector potential. -/ noncomputable def ofStaticVectorPotential {d} (c : SpeedOfLight) : ((Space d) →d[ℝ] EuclideanSpace ℝ (Fin d)) →ₗ[ℝ] DistElectromagneticPotential d := ofVectorPotential c ∘ₗ Space.constantTime TODO "Add a constructor for DistElectromagneticPotential from electric and magnetic f...
Exact Lean statement
@[simp]
lemma distTensorDeriv_basis_repr_apply {d} {μν : (Fin 1 ⊕ Fin d) × (Fin 1 ⊕ Fin d)}
(A : DistElectromagneticPotential d)
(ε : 𝓢(SpaceTime d, ℝ)) :
(Lorentz.CoVector.basis.tensorProduct Lorentz.Vector.basis).repr (distTensorDeriv A ε) μν =
distDeriv μν.1 A ε μν.2Formal artifact
Lean source
@[simp]lemma distTensorDeriv_basis_repr_apply {d} {μν : (Fin 1 ⊕ Fin d) × (Fin 1 ⊕ Fin d)} (A : DistElectromagneticPotential d) (ε : 𝓢(SpaceTime d, ℝ)) : (Lorentz.CoVector.basis.tensorProduct Lorentz.Vector.basis).repr (distTensorDeriv A ε) μν = distDeriv μν.1 A ε μν.2 := by match μν with | (μ, ν) => rw [distTensorDeriv_eq_sum_sum] simp only [map_sum, map_smul, Finsupp.coe_finsetSum, Finsupp.coe_smul, Finset.sum_apply, Pi.smul_apply, Basis.tensorProduct_repr_tmul_apply, Basis.repr_self, smul_eq_mul] rw [Finset.sum_eq_single μ, Finset.sum_eq_single ν] · simp · intro μ' _ h simp [h] · simp · intro ν' _ h simp [h] · simp- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Electromagnetism/Distributional/Basic.lean:166-184
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