Manuscript Oai119-A@1 · Oai119-A.tex · section · fdff7292

Gate 3: dimension induction and classical semigroup

Stage 1: the five proof interfaces › Gate 3: dimension induction and classical semigroup · lines 571–582

For a field $g$ , define the number operator

N g (x) = \frac{1}{2} i = 1 \sum^{n} (g (x) - g (x^{(i)})),

where $x^{(i)}$ flips coordinate $i$ . For interior $g$ , put

D (g) = E [atanh (g) N g] .

Displayed formulas in this passage

unlabeled · line 574
$N g (x) = \frac{1}{2} i = 1 \sum^{n} (g (x) - g (x^{(i)})),$
unlabeled · line 579
$D (g) = E [atanh (g) N g] .$