Relativistic CalogeroMoser systems and solutions
Abstract
Results pertaining to a class of completely integrable Nparticle systems, which generalize the CalogeroMoser (CM) systems, are reviewed. The systems are relativistically invariant, and the CM systems result from taking a parameter to infinity, which may be regarded as the speed of light. They can be quantized in such a fashion that integrability is preserved. However, only the classical level is discussed. A matrix whose symmetric functions yield N independent commuting Hamiltonians is used to construct the actionangle map. The relation of the particle systems to soliton equations is analyzed. Solutions consisting of solitons, antisolitons, breathers, etc... may all be viewed as manifestations of underlying point particle dynamics associated with the systems. The relation leads to a natural concept of soliton spacetime trajectory.
 Publication:

Unknown
 Pub Date:
 January 1987
 Bibcode:
 1987rcms.rept.....R
 Keywords:

 Invariance;
 Parameterization;
 Relativistic Particles;
 Relativistic Theory;
 Solitary Waves;
 Hamiltonian Functions;
 Partial Differential Equations;
 Particle Theory;
 Relativity;
 Wave Equations;
 Thermodynamics and Statistical Physics