Manuscript VII-F-ST@1 · VII-F-ST.tex · section · 9eee7a44

The exact transverse family and its product lift

The exact transverse family and its product lift · lines 437–459

VII-F-ST@1#eq:intersection

The radial collar

7/2 \leq ρ \leq 4, ∣ ζ ∣ \leq Z

is regular and horizontal at $t = 2 + s$ . The exterior has fixed spatial cells and fixed gluing, translated according to this prescribed equation. It is not the same embedded subset for all $s$ .

The singular intersection is

Σ_{s} \cap W = {(T_{*} + ℓ p (s) / c, o, z) : z \in R}, p (s) = {s, 2 s, s \leq 0, s \geq 0.

In a transverse section this is the source's particle point. In $3 + 1$ dimensions it is a line in a worldsheet.

Displayed formulas in this passage

VII-F-ST@1#eq:intersection · line 449
$Σ_{s} \cap W = {(T_{*} + ℓ p (s) / c, o, z) : z \in R}, p (s) = {s, 2 s, s \leq 0, s \geq 0.$
unlabeled · line 440
$7/2 \leq ρ \leq 4, ∣ ζ ∣ \leq Z$

Nearby in this section

section: The exact transverse family and its product lift
lemma: Lemma: Active region
theorem: Theorem: Embedded, uniformly spacelike ordered lift