Manuscript Em03-G@1 · Em03-G-v1.tex · proposition · 0bb3a8a3

Proposition: Spacelike observation invariance

Causality, interference energy, and switching work › Causal support · lines 1855–1872 · proof included or linked

Em03-G@1#prop:causality

If a compact local field test $G$ is spacelike separated from $supp F_{1} \cup supp F_{2}$ , then

U_{G}^{†} (I \otimes W (k_{G})) U_{G} = I \otimes W (k_{G}) .

Before the first slab the propagator is identity; between slabs only the first endpoint has acted.

Proof. Causal support gives $s (k (F_{j}), k_{G}) = \int F_{j} E G d vol_{g} = 0$ . Each controlled Weyl factor therefore commutes with the observable. The chronological assertions follow from the disjoint switching supports and Theorem thm:unitary.

Displayed formulas in this passage

unlabeled · line 1859
$U_{G}^{†} (I \otimes W (k_{G})) U_{G} = I \otimes W (k_{G}) .$

Nearby in this section

section: Causal support