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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 | | 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 $phi^4$ 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 | | Services: | Forum | Review | PDF | Favorites | |
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