Research proof index

The electromagnetic potential of a point particle stationary at r₀ of 3d space. -/ noncomputable def threeDimPointParticle (𝓕 : FreeSpace) (q : ℝ) (r₀ : Space 3) : DistElectromagneticPotential 3 := (SpaceTime.distTimeSlice 𝓕.c).symm <| Space.constantTime <| distOfFunction (fun x => (((q * 𝓕.μ₀ * 𝓕.c)/ (4 * π)) * ‖x - r₀‖⁻¹) • Lorentz.Vector.basis (S...

The electromagnetic potential of a point particle stationary at r₀ of 3d space. -/ noncomputable def threeDimPointParticle (𝓕 : FreeSpace) (q : ℝ) (r₀ : Space 3) : DistElectromagneticPotential 3 := (SpaceTime.distTimeSlice 𝓕.c).symm <| Space.constantTime <| distOfFunction (fun x => (((q * 𝓕.μ₀ * 𝓕.c)/ (4 * π)) * ‖x - r₀‖⁻¹) • Lorentz.Vector.basis (S...

The electromagnetic potential of a point particle stationary at r₀ of 3d space. -/ noncomputable def threeDimPointParticle (𝓕 : FreeSpace) (q : ℝ) (r₀ : Space 3) : DistElectromagneticPotential 3 := (SpaceTime.distTimeSlice 𝓕.c).symm <| Space.constantTime <| distOfFunction (fun x => (((q * 𝓕.μ₀ * 𝓕.c)/ (4 * π)) * ‖x - r₀‖⁻¹) • Lorentz.Vector.basis (S...

The current density of a point particle stationary at a point r₀ of 3d space. -/ noncomputable def threeDimPointParticleCurrentDensity (c : SpeedOfLight) (q : ℝ) (r₀ : Space 3) : DistLorentzCurrentDensity 3 := (SpaceTime.distTimeSlice c).symm <| constantTime ((c * q) • diracDelta' ℝ r₀ (Lorentz.Vector.basis (Sum.inl 0))) lemma threeDimPointParticleCurre...