Solutions of the Hamilton--Jacobi equation for one component two dimensional Field Theories

Details Solutions of the Hamilton--Jacobi equation for one component two dimensional Field Theories Solutions of the Hamilton--Jacobi equation for one component two dimensional Field Theories

1995-01-25

arxiv.org/abs/hep-th/9501115v1

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, no figures

Scientific paper

The 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. B\"acklund Transformations play a crucial role in solving the resulting system of coupled nonlinear PDEs.

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