Research proof index

The electromagnetic potential of an infinite wire along the x-axis carrying a current I. -/ noncomputable def infiniteWire (𝓕 : FreeSpace) (I : ℝ) : DistElectromagneticPotential 3 := (SpaceTime.distTimeSlice 𝓕.c).symm <| constantTime <| constantSliceDist 0 ((- I * 𝓕.μ₀ / (2 * Real.pi)) • distOfFunction (fun (x : Space 2) => Real.log ‖x‖ • Lorentz.Vec...

The proposition on an electromagnetic potential, corresponding to the statement that it is an extrema of the lagrangian. -/ def IsExtrema {d} (𝓕 : FreeSpace) (A : DistElectromagneticPotential d) (J : DistLorentzCurrentDensity d) : Prop := A.gradLagrangian 𝓕 J = 0 lemma isExtrema_iff_gradLagrangian {𝓕 : FreeSpace} (A : DistElectromagneticPotential d) (J...

The magnetic field matrix of an electromagnetic potential which is a distribution. -/ noncomputable def magneticFieldMatrix {d} (c : SpeedOfLight) : DistElectromagneticPotential d →ₗ[ℝ] (Time × Space d) →d[ℝ] (EuclideanSpace ℝ (Fin d) ⊗[ℝ] EuclideanSpace ℝ (Fin d)) where toFun A := ⟨TensorProduct.map (Lorentz.Vector.spatialCLM d).toLinearMap (Lorentz.Vect...

The magnetic field matrix of an electromagnetic potential which is a distribution. -/ noncomputable def magneticFieldMatrix {d} (c : SpeedOfLight) : DistElectromagneticPotential d →ₗ[ℝ] (Time × Space d) →d[ℝ] (EuclideanSpace ℝ (Fin d) ⊗[ℝ] EuclideanSpace ℝ (Fin d)) where toFun A := ⟨TensorProduct.map (Lorentz.Vector.spatialCLM d).toLinearMap (Lorentz.Vect...

The electromagnetic potential of a point particle stationary at r₀ of 1d space. -/ noncomputable def oneDimPointParticle (𝓕 : FreeSpace) (q : ℝ) (r₀ : Space 1) : DistElectromagneticPotential 1 := (SpaceTime.distTimeSlice 𝓕.c).symm <| Space.constantTime <| distOfFunction (fun x => ((- (q * 𝓕.μ₀ * 𝓕.c)/ 2) * ‖x - r₀‖) • Lorentz.Vector.basis (Sum.inl 0...

The electromagnetic potential of a point particle stationary at r₀ of 1d space. -/ noncomputable def oneDimPointParticle (𝓕 : FreeSpace) (q : ℝ) (r₀ : Space 1) : DistElectromagneticPotential 1 := (SpaceTime.distTimeSlice 𝓕.c).symm <| Space.constantTime <| distOfFunction (fun x => ((- (q * 𝓕.μ₀ * 𝓕.c)/ 2) * ‖x - r₀‖) • Lorentz.Vector.basis (Sum.inl 0...