Manuscript X-A-ST@1 · X-A-ST.tex · definition · d9ccbde1

Definition: Coordinate Cauchy prescription

Frozen classical prescription › Two different density operators · lines 595–610

X-A-ST@1#def:coordinates, X-A-ST@1#eq:coordinateproblem

The four components of

Co_{q}^{μ} = x^{μ} + κ w^{μ} + κ^{2} v^{μ}

are scalar functions satisfying

D_{ε} [q] Co_{q}^{μ} = 0 (mod κ^{3}), Co_{q}^{μ} ∣_{Σ} = x^{μ} ∣_{Σ}, \partial_{t} Co_{q}^{μ} ∣_{Σ} = δ^{μ}_{0} .

The component label $μ$ does not prescribe a vector-field pullback. The switch $g$ does not enter this problem.

Displayed formulas in this passage

X-A-ST@1#eq:coordinateproblem · line 602
$D_{ε} [q] Co_{q}^{μ} = 0 (mod κ^{3}), Co_{q}^{μ} ∣_{Σ} = x^{μ} ∣_{Σ}, \partial_{t} Co_{q}^{μ} ∣_{Σ} = δ^{μ}_{0} .$
unlabeled · line 598
$Co_{q}^{μ} = x^{μ} + κ w^{μ} + κ^{2} v^{μ}$