New Types of the Lie Symmetries and Conserved Quantities for a Relativistic Hamiltonian System

For a relativistic Hamiltonian system,two new types of the Lie symmetries and conservation laws are given under infinitesimal transformaitons of groups.On the basis of the theory of invariance of the relativistic Hamiltonian equations under infinitesimal transformations and introducing infinitesimal transformations for time t,generalized coordinates qs and generalized monenta ps,we obtain the determinging equations,the structure equations and the conserved quantities of the Lie symmetries.Introducing infinitesimal transformation for generalized coordinates qs and generalized momenta ps,we construct the Lie symmetrical transformations of the system,which only depend on the canonical variables.A set of conserved quantities are directly obtained from the Lie symmetries of the syste.An example is given to illustrante the application of the results.