Classical integrable field theories in discrete 2+1 dimensional space-time

Details Classical integrable field theories in discrete 2+1 dimensional space-time Classical integrable field theories in discrete 2+1 dimensional space-time

2009-02-25

arxiv.org/abs/0902.4265v1

J.Phys.A42:295206,2009

Nonlinear Sciences

Exactly Solvable and Integrable Systems

22 pages

Scientific paper

10.1088/1751-8113/42/29/295206

We study "circular net" (discrete orthogonal net) equations for angular data generalized by external spectral parameters. A criterion defining physical regimes of these Hamiltonian equations is the reality of Lagrangian density. There are four distinct regimes for fields and spectral parameters classified by four types of spherical or hyperbolic triangles. Non-zero external spectral parameters provide the existence of field-theoretical ground states and soliton excitations. Spectral parameters of a spherical triangle correspond to a statistical mechanics; spectral parameters of hyperbolic triangles correspond to three different field theories with massless anisotropic dispersion relations.

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