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

Abstract

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 qs and ps, 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.