Relativistic Calogero-Moser systems and solutions
Abstract
Results pertaining to a class of completely integrable N-particle systems, which generalize the Calogero-Moser (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 action-angle 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 space-time trajectory.
- Publication:
-
Unknown
- Pub Date:
- January 1987
- Bibcode:
- 1987rcms.rept.....R
- Keywords:
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- Invariance;
- Parameterization;
- Relativistic Particles;
- Relativistic Theory;
- Solitary Waves;
- Hamiltonian Functions;
- Partial Differential Equations;
- Particle Theory;
- Relativity;
- Wave Equations;
- Thermodynamics and Statistical Physics