Manuscript XI-G@1 · XI-G.tex · definition · f029bbcd

Definition: Bilinear symbol

G1: Cauchy reduction of the onset › The bilinear symbol and its counter-propagating values · lines 774–782

XI-G@1#def:symbol

For constant symmetric $ϵ_{1}, ϵ_{2}$ and vectors $k_{1}, k_{2}$ let $q^{μν} (ϵ_{1}, k_{1}; ϵ_{2}, k_{2})$ be defined by

J_{3}^{μν} (ϵ_{1} e^{i k_{1} \cdot y}, ϵ_{2} e^{i k_{2} \cdot y}) = q^{μν} (ϵ_{1}, k_{1}; ϵ_{2}, k_{2}) e^{i (k_{1} + k_{2}) \cdot y} .

Displayed formulas in this passage

unlabeled · line 778
$J_{3}^{μν} (ϵ_{1} e^{i k_{1} \cdot y}, ϵ_{2} e^{i k_{2} \cdot y}) = q^{μν} (ϵ_{1}, k_{1}; ϵ_{2}, k_{2}) e^{i (k_{1} + k_{2}) \cdot y} .$