Scattering and complete integrability in the massive \(\phi ^ 4\) theory
The wave and scattering operators for the equation \[ (\square +m^ 2)\phi +\lambda \phi^ 3=0,\quad m>0,\quad \lambda \geq 0,\quad x\in {\mathbb{R}}^ 3, \] are defined by comparison of the asymptotics as \(t\to \pm \infty\) of its solutions with that for the Klein-Gordon equation \((\lambda =0)\). The basic result is analyticity of the wave and scattering operators for small finite-energy Cauchy data. Complete integrability of the massive \(\phi^ 4\) theory at low energy is discussed.
Complete integrability of the massive \(\phi ^ 4\) theory at low energy
scientific article; zbMATH DE number 4205165