A set of Lie symmetrical non-Noether conserved quantity for the relativistic Hamiltonian systems

For the relativistic Hamiltonian system, a new type of Lie symmetrical non-Noether conserved quantities are given. On the basis of the theory of invariance of differential equations under infinitesimal transformations, and introducing special infinitesimal transformations for q_s and p_s, we construct the determining equations of Lie symmetrical transformations of the system, which only depend on the canonical variables. A set of non-Noether conserved quantities are directly obtained from the Lie symmetries of the system. An example is given to illustrate the application of the results.