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 transformations 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 q_s and generalized momentums p_s, we obtain the determining equations, the structure equations and the conserved quantities of the Lie symmetries. Introducing infinitesimal transformation for generalized coordinates q_s and generalized momentums p_s, 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 system. An example is given to illustrate the application of the results.