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

Formal fields and density coefficients

Frozen classical prescription › Formal fields and density coefficients · lines 468–483

X-A-ST@1#eq:CK, X-A-ST@1#eq:CKidentity

Define

C^{μ} [h] = \partial_{ν} h^{ν μ} - \frac{1}{2} \partial^{μ} H = - \partial_{ν} a_{1}^{ν μ} [h], (K ξ)_{μν} = \partial_{μ} ξ_{ν} + \partial_{ν} ξ_{μ} .

A direct calculation gives

C^{μ} [K ξ] = □ ξ^{μ} .

Displayed formulas in this passage

X-A-ST@1#eq:CK · line 471
$C^{μ} [h] = \partial_{ν} h^{ν μ} - \frac{1}{2} \partial^{μ} H = - \partial_{ν} a_{1}^{ν μ} [h], (K ξ)_{μν} = \partial_{μ} ξ_{ν} + \partial_{ν} ξ_{μ} .$
X-A-ST@1#eq:CKidentity · line 479
$C^{μ} [K ξ] = □ ξ^{μ} .$