  Symplectic schemes are powerful methods for numerically integrating
Hamiltonian systems, and their long-term accuracy and fidelity have been proved
both theoretically and numerically. However direct applications of standard
symplectic schemes to relativistic charged particle dynamics result in implicit
and electromagnetic gauge-dependent algorithms. In the present study, we
develop explicit high-order gauge-independent noncanonical symplectic
algorithms for relativistic charged particle dynamics using a Hamiltonian
splitting method in the 8D phase space. It also shown that the developed
algorithms can be derived as variational integrators by appropriately
discretizing the action of the dynamics. Numerical examples are presented to
verify the excellent long-term behavior of the algorithms.
