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08 July 2020
  » arxiv » hep-th/9501115

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Solutions of the Hamilton--Jacobi equation for one component two dimensional Field Theories
Wulf Boettger ; Henning Wissowski ; Hans A. Kastrup ;
Date 25 Dec 1994
Subject High Energy Physics - Theory; Functional Analysis | hep-th cond-mat funct-an gr-qc math.FA
AbstractThe Hamilton--Jacobi formalism generalized to 2--dimensional field theories according to Lepage’s canonical framework is applied to several covariant real scalar fields, e.g. massless and massive Klein--Gordon, Sine--Gordon, Liouville and $phi^4$ theories. For simplicity we use the Hamilton--Jacobi equation of DeDonder and Weyl. Unlike mechanics we have to impose certain integrability conditions on the velocity fields to guarantee the transversality relations between Hamilton--Jacobi wave fronts and the corresponding families of extremals embedded therein. Bäcklund Transformations play a crucial role in solving the resulting system of coupled nonlinear PDEs.
Source arXiv, hep-th/9501115
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