Manuscript VIII-ST@1 · VIII-ST.tex · section · fe979f3b

Packet and chart conventions

Lorentz-affine matching and complete certificates › Packet and chart conventions · lines 880–896

VIII-ST@1#eq:transition

These affine formulas extend algebraically to face closures. They do not make the apex a regular Minkowski point.

For an oriented overlap component $f \to g$ , let $n_{g f} \in {- 1, 0, 1}$ record its marked seam crossing. The canonical transition is

T_{g \leftarrow f} = A_{g} J_{μ}^{n_{g f}} A_{f}^{- 1} .

A longer path retains the ordered components and all exponents. Agreement on only the endpoints of an edge is weaker than (eq:transition): a nontrivial Lorentz transformation can fix a spacelike line pointwise.

Displayed formulas in this passage

VIII-ST@1#eq:transition · line 888
$T_{g \leftarrow f} = A_{g} J_{μ}^{n_{g f}} A_{f}^{- 1} .$

Nearby in this section

section: Packet and chart conventions
lemma: Lemma: Spinless fixed set
section: Packet and chart conventions
lemma: Lemma: Adapted charts
definition: Definition: Five-component acceptance
theorem: Theorem: Complete matching for the explicit family
section: Packet and chart conventions
proposition: Proposition: Fixed-presentation uniqueness and two rejection tests