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

Wulf Boettger·Henning Wissowski·Hans A. Kastrup
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Abstract

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 $ϕ^4$ 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.

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Wulf Boettger, Henning Wissowski, Hans A. Kastrup. 1995-01-25. Solutions of the Hamilton--Jacobi equation for one component two dimensional Field Theories. https://arxiv.org/abs/hep-th/9501115

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