Analyticity of the scattering operator for the nonlinear Klein-Gordon equation with cubic nonlinearity
type: Item
instance of: scholarly article
title: Analyticity of the scattering operator for the nonlinear Klein-Gordon equation with cubic nonlinearity
zbMATH Open document ID: 0749.35045
DOI: 10.1007/BF02101092
author: Peter Kumlin
published in: Communications in Mathematical Physics
publication date: 1992-09-26T00:00:00Z
review text: This paper answers a question, raised by \textit{J. C. Baez} and \textit{Z.-F. Zhou} [(*) J. Funct. Anal. 94, No. 2, 397-414 (1990; Zbl 0729.47009)] whether the scattering and wave operators for \[ (\square+m^ 2)\varphi+\lambda\varphi^ 3=0,\quad m>0,\quad\lambda>0, \] are analytic or not on the whole space of finite-energy data \(L^ 1_ 2(\mathbb{R}^ 3)\oplus L_ 2(\mathbb{R}^ 3)\). The answer is affirmative. This implies, which is noted in (*), that the massive \(\varphi^ 4\) theory is completely integrable. The same holds for the massless \(\varphi^ 4\) theory proved by \textit{J. C. Baez} [J. Math. Phys. 31, No. 3, 757-762 (1990; Zbl 0715.58035)].
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
zbMATH DE Number: 54745
zbMATH Keywords: finite energy Cauchy data
zbMATH Keywords: complete integrability
zbMATH Keywords: phi(sup4)-theory
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 54745