Manuscript XVI-I@1 · XVI-I.tex · section · a7046a8d

Jet-coordinate definition of the Hessian

The cubic interaction and its exact jet Hessian › Jet-coordinate definition of the Hessian · lines 886–901

XVI-I@1#eq:L

Write $h_{K, a} = \partial^{a} h_{K}$ , where the multiindices label independent symmetric jet coordinates. Define

L_{K L; ab} [h] (w) = \frac{\partial ^{2} ℓ _{3}}{\partial h _{K, a} \partial h _{L, b}}_{j^{2} h (w)} .

Absent jet variables have zero coefficient.

Displayed formulas in this passage

XVI-I@1#eq:L · line 891
$L_{K L; ab} [h] (w) = \frac{\partial ^{2} ℓ _{3}}{\partial h _{K, a} \partial h _{L, b}}_{j^{2} h (w)} .$