Manuscript Oai282-A@1 · Oai282-A.tex · section · 5b6134ec

Conformal-Killing currents

Stage 2: conditional improvement and its affine charges › Conformal-Killing currents · lines 633–645

A conformal Killing field satisfies

\partial_{μ} X_{ν} + \partial_{ν} X_{μ} = 2 σ_{X} η_{μν}, σ_{X} = \frac{1}{4} \partial_{ρ} X^{ρ} .

Translations and Lorentz transformations have $σ_{X} = 0$ ; dilations have $σ_{X} = 1$ ; special conformal fields have $σ_{X_{b}} = 2 b \cdot x$ .

Displayed formulas in this passage

unlabeled · line 636
$\partial_{μ} X_{ν} + \partial_{ν} X_{μ} = 2 σ_{X} η_{μν}, σ_{X} = \frac{1}{4} \partial_{ρ} X^{ρ} .$