Manuscript VII-E-ST@1 · VII-E-ST.tex · section · d28d9c5d

A genuinely supported 3+1-dimensional marking

A four-face certificate and its supported 3+1 lift › A genuinely supported 3+1-dimensional marking · lines 984–1007

For an affine piece $t = v \cdot x + β (s)$ , a fully specified adapted chart is the standard Lorentz boost

B_{v}^{0} = γ_{v} (t - v \cdot x), B_{v}^{sp} = x + [\frac{γ _{v} - 1}{∣ v ∣ ^{2}} (v \cdot x) - γ_{v} t] v, γ_{v} = (1 - ∣ v ∣^{2})^{- 1/2},

followed by time translation $(s - γ_{v} β (s)) e_{0}$ . For $v = 0$ , use its continuous identity-boost value. Thus every lifted piece has an explicit affine chart, and all closed transition products still telescope.

The four-face statement concerns the transverse section $∣ z ∣ \leq 1$ . In the full lift its junction is extended in the axial direction. We do not relabel it as an isolated $3 + 1$ -dimensional particle event, nor claim a catalogue of all additional taper incidences.

Displayed formulas in this passage

unlabeled · line 988
$B_{v}^{0} = γ_{v} (t - v \cdot x), B_{v}^{sp} = x + [\frac{γ _{v} - 1}{∣ v ∣ ^{2}} (v \cdot x) - γ_{v} t] v, γ_{v} = (1 - ∣ v ∣^{2})^{- 1/2},$

A genuinely supported 3+1-dimensional marking

Displayed formulas in this passage

Nearby in this section