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[We provide an historical overview the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi ^4$$\end{document} model, placing it in the broad context of general KG theories and reviewing its applications to physics. While we will mention briefly other variants of the KG theory, we will focus chiefly on the history of the one-space, one-time dimensional [(1+1)D] degenerate minimum \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi ^4$$\end{document} theory that is the central topic of this book. We will also compare this theory to other nonlinear Klein–Gordon equations, in particular, to the celebrated sine-Gordon theory. We review in some detail the history of the interrelated dynamical problems of kink-antikink scattering, contrasting \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi ^4$$\end{document} and other non-integrable models with sine-Gordon and the search for a possible “breather” solution to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi ^4$$\end{document} in the continuum limit. Our discussion is intended to set the stage for more detailed expositions in the later chapters.]
Published: Feb 27, 2019
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