Independence up to isomorphism

This proves independence of the algebra up to isomorphism, not equality of all normal-ordering formulas. In particular, a cubic normally ordered symbol can acquire an order-$\hslash$ linear term under ${\alpha }_d$. A transported admission is ${\alpha }_d{Q}_H(F)$; the separately written $Q_{H^{\prime }}(F)$ need not be that same abstract element without a normalization convention. At ${\hslash }^0$ their symbols agree. The scalar extended-Wick comparison is also expressed in HW (Lemma 2.1).

No state was needed for these statements. Conversely, a loop coefficient can depend on the smooth product data even when no expectation value is taken.