Mechanical Systems with Poincare Invariance

Details Mechanical Systems with Poincare Invariance Mechanical Systems with Poincare Invariance

2001-10-09

arxiv.org/abs/nlin/0110014v1

Phys.Lett. A295 (2002) 208-216

Nonlinear Sciences

Exactly Solvable and Integrable Systems

10 pages LaTex, 1 figure

Scientific paper

10.1016/S0375-9601(02)00160-3

Some years ago Ruijsenaars and Schneider initiated the study of mechanical systems exhibiting an action of the Poincare algebra. The systems they discovered were far richer: their models were actually integrable and possessed a natural quantum version. We follow this early work finding and classifying mechanical systems with such an action. New solutions are found together with a new class of models exhibiting an action of the Galilean algebra. These are related to the functional identities underlying the various Hirzebruch genera. The quantum mechanics is also discussed.

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