Manuscript Oai282-B@1 · Oai282-B.tex · section · f2956de5

The original bounded net

The free model, its test topology, and its domain › The original bounded net · lines 335–350

Oai282-B@1#eq:net

For every bounded open region $O$ , define

A (O) = {e^{i ϕ (f)} : f \in C_{c}^{\infty} (O; R)}^{''} .

The closure of $ϕ (f)$ is self-adjoint for real $f$ : finite-particle vectors are analytic for a Segal field. The same creation–annihilation calculation gives locality from (eq:CCR). Thus (eq:net) is the original scalar Weyl net, not a net enlarged by adjoining $Q$ .

Displayed formulas in this passage

Oai282-B@1#eq:net · line 338
$A (O) = {e^{i ϕ (f)} : f \in C_{c}^{\infty} (O; R)}^{''} .$