A New Type of Symmetry,i.e.the Mei Symmetry,of the Relativistic Hamiltonian Systems

【摘要】：正For a relativistic Hamiltonian system,a new type of symmetry,i.e.the Mei symmetry,of the relativistic Hamiltonian canonical equations in phase space is constructed.The definition and the determining equations of the Mei symmetry of the system are given under the infinitesimal transformations of groups.The relations among the Mei symmetry,the Noether symmetry and the Lie symmetry are studied,and the conserved quantities of the system are obtained.Under the infinitesimal transformations of the relativistic Hamiltonian H,if the form of the relativistic Hamiltonian canonical equations remains invariant,then the system has the Mei symmetry.Furthermore,for the infinitesimal generators ξ_0,ξ_s and η_s satisfying the relativistic Mei symmetry determining equations,if there exists a gauge function G(t,q,,p_s)such that the relativistic generalized Noether identities hold,then the Mei symmetry will lead to a conserved quantity of the system.An example is given to illustrate the application of the results.

【基金】：Project supported by the National Natural Science Foundation of China(Grant No 10372053) the Natural Science foundation of Hunan Province(Grant No 03JJY3005) the Scientific Research Foundation of the Education Bureau of Hunan Province(Grant No.02C033).
【分类号】：O316