Manuscript III@2 · III.tex · proposition · 82dad3e5

Proposition: Temporal dressing in canonical variables

What instantaneous Poisson compensation establishes › Canonical temporal normalization · lines 2368–2390 · proof included or linked

III@2#prop:ADM

Back to manuscript

For this normalization,

π^{ij} = v_{ij} - δ^{ij} v_{k k}, Π_{tr} := π^{ii} = - 2 h ˙_{ii} + 4 \partial_{i} h_{0 i} .

Thus

Π_{tr} = 4 B_{P} [h], w_{P}^{0} = \frac{1}{4} N Π_{tr} .

Proof. Differentiate the kinetic density with the symmetric-tensor convention, and take its spatial trace. Then $π^{ii} = - 2 v_{ii}$ . Use the definition of $B_{P}$ .

Displayed formulas in this passage

unlabeled · line 2371
$π^{ij} = v_{ij} - δ^{ij} v_{k k}, Π_{tr} := π^{ii} = - 2 h ˙_{ii} + 4 \partial_{i} h_{0 i} .$
unlabeled · line 2378
$Π_{tr} = 4 B_{P} [h], w_{P}^{0} = \frac{1}{4} N Π_{tr} .$

Nearby in this section

section: Canonical temporal normalization
section: Canonical temporal normalization