Manuscript X-A@1 · X-A.tex · definition · dc7f5c0a

Definition: Relational scalar and observable

Relational expansion and insertion signs · lines 1367–1380

X-A@1#def:observable, X-A@1#eq:observable

For $(h, k, ϕ) \in C$ ,

Φ_{g, ε} [q, ϕ] (z) = ϕ (X_{q}^{- 1} (z)), O_{f, g, ε} [q, ϕ] = \int f (z) Φ_{g, ε} [q, ϕ] (z) d^{4} z \in D_{2} .

The subscript $g$ records that the on-shell evaluation of Definition def:rho uses $g$ ; the functional itself depends on $g$ only through that evaluation.

Displayed formulas in this passage

X-A@1#eq:observable · line 1370
$Φ_{g, ε} [q, ϕ] (z) = ϕ (X_{q}^{- 1} (z)), O_{f, g, ε} [q, ϕ] = \int f (z) Φ_{g, ε} [q, ϕ] (z) d^{4} z \in D_{2} .$

Nearby in this section

lemma: Lemma: Formal inverse
lemma: Lemma: Expansion and insertion signs
section: Relational expansion and insertion signs