Manuscript X-E@1 · X-E.tex · definition · 293fae6a

Definition

E3: the quadratic operator, its inverse, and the residual algebra › De Donder gauge fixing and the operator · lines 1031–1040

X-E@1#def:gf

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$h ˉ_{μν} = h_{μν} - \frac{1}{2} η_{μν} H$ , $P h := h ˉ$ , $C^{μ} [h] = \partial_{ν} h ˉ^{ν μ} = \partial_{ν} h^{ν μ} - \frac{1}{2} \partial^{μ} H$ , $S_{gf} [h] = \frac{1}{4} \int C_{μ} C^{μ}$ . Note $h ˉ^{μν} = - a_{1}^{μν} [h]$ and $C^{μ} [h] = - \partial_{ν} a^{ν μ} [h]$ : the de Donder vector is X-A's coordinate source without the ramp.

Nearby in this section

lemma: Lemma: Gauge-fixed operator
lemma: Lemma: De Donder violation of a retarded response