Manuscript IX-A@1 · IX-A.tex · section · 55aa6f6d

Formal coefficient slots through the first obstructed order

Faithfulness, classical presentation independence, and formal slots › Formal coefficient slots through the first obstructed order · lines 1668–1691

IX-A@1#eq:module

Define the locally convex module

V_{Σ}^{[3]} = P_{Σ} \otimes_{C} C [ℏ] / (ℏ^{4}) ≃ P_{Σ}^{4},

with the finite product topology. Define

cl (r = 0 \sum^{3} ℏ^{r} F_{r}) = F_{0} .

The map $cl$ and field-independent coefficient evaluations are continuous.

The old bulk quantum algebra

P_{mc} \otimes_{C} C [ℏ] / (ℏ^{4})

embeds linearly and injectively in $V_{Σ}^{[3]}$ . Its old product remains prescribed on that subspace.

Displayed formulas in this passage

IX-A@1#eq:module · line 1671
$V_{Σ}^{[3]} = P_{Σ} \otimes_{C} C [ℏ] / (ℏ^{4}) ≃ P_{Σ}^{4},$
unlabeled · line 1679
$cl (r = 0 \sum^{3} ℏ^{r} F_{r}) = F_{0} .$
unlabeled · line 1686
$P_{mc} \otimes_{C} C [ℏ] / (ℏ^{4})$