Manuscript XIII-D@1 · XIII-D.tex · input · bab69024

Input statement: Restriction handoff

Copied prerequisite sheet › XIII-A: evaluation and the non-ideal boundary · lines 306–332

Under $(UCP_{W})$ ,

Δ_{ξ} O_{C_{W}} = 0, ξ \in C_{c}^{\infty} (W; T M),

with

W \subset int {g = 1} \cap {ε < t < T}, C_{W} = {u \in C_{sol} : D^{*} b = 0 on W} .

The coefficientwise kernel $N_{W}$ is not a two-sided ideal: compact tests give

[L_{q}, G_{h}]_{⋆_{H}} = i ℏ C (q, h) 1, C (q, h) > 0,

and an admissible rank-one ordering change satisfies

α_{d} (L_{q}^{2}) = L_{q}^{2} + ℏ L_{q} (u)^{2} .

Forcing $ℏ 1 = 0$ does not force $1 = 0$ over $C [[ℏ]]$ . It does rule out a torsion-free formal quantum quotient with the inherited brackets. No reduced algebra was handed off XIIIA.

Displayed formulas in this passage

unlabeled · line 308
$Δ_{ξ} O_{C_{W}} = 0, ξ \in C_{c}^{\infty} (W; T M),$
unlabeled · line 313
$W \subset int {g = 1} \cap {ε < t < T}, C_{W} = {u \in C_{sol} : D^{*} b = 0 on W} .$
unlabeled · line 320
$[L_{q}, G_{h}]_{⋆_{H}} = i ℏ C (q, h) 1, C (q, h) > 0,$
unlabeled · line 325
$α_{d} (L_{q}^{2}) = L_{q}^{2} + ℏ L_{q} (u)^{2} .$

Nearby in this section

section: XIII-A: evaluation and the non-ideal boundary