Manuscript Hawk05-C@1 · Hawk05-C.tex · section · ba0719f1

Conserved-sector scrambling: a direct-sum Page calculation

Conserved-sector scrambling: a direct-sum Page calculation · lines 1396–1423

Hawk05-C@1#eq:charge-sector

A conserved total additive charge need not leave a tensor-product sector. At a cut, suppose the justified sector is

H_{q} = λ ⨁ (R_{λ} \otimes B_{q - λ}),

embedded in the physical tensor product. Distinct $λ$ have orthogonal radiation charge sectors and orthogonal residual charge sectors. Retain only nonzero blocks, and set

r_{λ} = dim R_{λ}, b_{λ} = dim B_{q - λ}, D_{λ} = r_{λ} b_{λ}, D_{q} = λ \sum D_{λ},

w_{λ} = \frac{D _{λ}}{D _{q}}, m_{λ} = min (r_{λ}, b_{λ}), n_{λ} = max (r_{λ}, b_{λ}) .

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Hawk05-C@1#eq:charge-sector · line 1401
$H_{q} = λ ⨁ (R_{λ} \otimes B_{q - λ}),$
unlabeled · line 1411
$r_{λ} = dim R_{λ}, b_{λ} = dim B_{q - λ}, D_{λ} = r_{λ} b_{λ}, D_{q} = λ \sum D_{λ},$
unlabeled · line 1417
$w_{λ} = \frac{D _{λ}}{D _{q}}, m_{λ} = min (r_{λ}, b_{λ}), n_{λ} = max (r_{λ}, b_{λ}) .$

Conserved-sector scrambling: a direct-sum Page calculation

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