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Clear filtersSpaceTime.deriv_commute
Project documentation
Derivatives on spacetime commute with one another (Clairaut's theorem).
Source project: Physlib
Person-level attribution pending.
SpaceTime.deriv_comp_lorentz_action
Project documentation
Derivatives on spacetime commute with one another (Clairaut's theorem). -/ lemma deriv_commute {M : Type} [NormedAddCommGroup M] [NormedSpace ℝ M] {d : ℕ} (μ ν : Fin 1 ⊕ Fin d) (f : SpaceTime d → M) (hf : ContDiff ℝ 2 f) : ∂_ μ (∂_ ν f) = ∂_ ν (∂_ μ f) := by ext x show fderiv ℝ (fun y => fderiv ℝ f y (Lorentz.Vector.basis ν)) x (Lorentz.Vector.basis μ) =...
Source project: Physlib
Person-level attribution pending.
SpaceTime.deriv_sum_inr
Project documentation
Derivatives on spacetime commute with one another (Clairaut's theorem). -/ lemma deriv_commute {M : Type} [NormedAddCommGroup M] [NormedSpace ℝ M] {d : ℕ} (μ ν : Fin 1 ⊕ Fin d) (f : SpaceTime d → M) (hf : ContDiff ℝ 2 f) : ∂_ μ (∂_ ν f) = ∂_ ν (∂_ μ f) := by ext x show fderiv ℝ (fun y => fderiv ℝ f y (Lorentz.Vector.basis ν)) x (Lorentz.Vector.basis μ) =...
Source project: Physlib
Person-level attribution pending.
SpaceTime.distDeriv_comp_lorentz_action
Project documentation
Given a distribution (function) f : Space d →d[ℝ] M the derivative of f in direction μ. -/ noncomputable def distDeriv {M d} [NormedAddCommGroup M] [NormedSpace ℝ M] (μ : Fin 1 ⊕ Fin d) : ((SpaceTime d) →d[ℝ] M) →ₗ[ℝ] (SpaceTime d) →d[ℝ] M where toFun f := let ev : (SpaceTime d →L[ℝ] M) →L[ℝ] M := { toFun v := v (Lorentz.Vector.basis μ) map_add' v1...
Source project: Physlib
Person-level attribution pending.