 Two coupled real Klein-Gordon fields

For interaction density $g{\varphi }_1{\varphi }_2$, the combinations ${\varphi }_{\pm }={\varphi }_1\pm {\varphi }_2$ diagonalize the equations into independent Klein-Gordon equations with the displayed mass squares. When $0<g<m^2$, all Fourier frequencies are real and nonzero. Initial data in one original field generally excite both normal combinations.