Manuscript XX-A@1 · XX-A.tex · lemma · 3a586110

Lemma: Formal-order separation

Formal quantum coefficient and the exact Ward-repair contract › Positive quantum powers do not repair a classical residual · lines 1437–1452 · proof included or linked

XX-A@1#lem:hbar

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Let $V$ be a vector space. If a Ward variation has the formal form

D = D_{cl} + ℏ D_{1} + ℏ^{2} D_{2} + \dots in V [[ℏ]],

and $D_{cl} \neq = 0$ , no addition belonging to $ℏ V [[ℏ]]$ can make it vanish.

Proof. The coefficient of $ℏ^{0}$ is unchanged by such an addition. Equality of formal series is coefficientwise equality.

Displayed formulas in this passage

unlabeled · line 1441
$D = D_{cl} + ℏ D_{1} + ℏ^{2} D_{2} + \dots in V [[ℏ]],$

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section: Positive quantum powers do not repair a classical residual