Research proof index

The time slice of a distribution on SpaceTime d to form a distribution on Time × Space d. -/ noncomputable def distTimeSlice {M d} [NormedAddCommGroup M] [NormedSpace ℝ M] (c : SpeedOfLight := 1) : ((SpaceTime d) →d[ℝ] M) ≃L[ℝ] ((Time × Space d) →d[ℝ] M) where toFun f := f ∘L compCLMOfContinuousLinearEquiv (F := ℝ) ℝ (SpaceTime.toTimeAndSpace c (d :=...

The equivalence on of SpaceTime taking (1, 0, 0, ...) to of (c, 0, 0, ....) and keeping all other components the same. -/ def timeSpaceBasisEquiv {d : ℕ} (c : SpeedOfLight) : SpaceTime d ≃L[ℝ] SpaceTime d where toFun x := fun μ => match μ with | Sum.inl 0 => c.val * x (Sum.inl 0) | Sum.inr i => x (Sum.inr i) invFun x := fun μ => match μ with | Sum.i...

The equivalence on of SpaceTime taking (1, 0, 0, ...) to of (c, 0, 0, ....) and keeping all other components the same. -/ def timeSpaceBasisEquiv {d : ℕ} (c : SpeedOfLight) : SpaceTime d ≃L[ℝ] SpaceTime d where toFun x := fun μ => match μ with | Sum.inl 0 => c.val * x (Sum.inl 0) | Sum.inr i => x (Sum.inr i) invFun x := fun μ => match μ with | Sum.i...

The generators of the clifford algebra correspond to the elements γ.

The central ℤ₆ subgroup acts trivially on (3, 1)_{-2}.

Characterizes the full-group elements acting trivially on the down-type singlet.