Manuscript XII-D@1 · XII-D.tex · proposition · 308a2080

Proposition: Existing, possibly nonzero divergence

D1: the smooth classical response › The response divergence · lines 569–586 · proof included or linked

XII-D@1#eq:response-divergence

The response satisfies

D^{ν} u_{D} = - E_{0}^{R} (\partial_{μ} J_{D}^{μν}) = \frac{1}{2} E_{0}^{R} (σ_{ε} Q^{ν} (A γ) - R_{σ_{ε}}^{ν} [γ]) .

Proof. Use $P^{2} = id$ in (eq:response), commute constant derivatives with the locally defined wave inverse, and apply (eq:source-divergence).

Displayed formulas in this passage

XII-D@1#eq:response-divergence · line 571
$D^{ν} u_{D} = - E_{0}^{R} (\partial_{μ} J_{D}^{μν}) = \frac{1}{2} E_{0}^{R} (σ_{ε} Q^{ν} (A γ) - R_{σ_{ε}}^{ν} [γ]) .$