Abstract
We study a new class of symplectic integrators for particles in arbitrary, time-dependent vector and scalar potentials. The methods were introduced in [Y.K. Wu, E. Forest, D.S. Robin, Phys. Rev. E 68 (2003) 046502] and are based on the ability to integrate Hamiltonians of the form ( p i − a i ( q ) ) 2 exactly for a finite time-step. We show that the integrators are symplectic in the non-relativistic case but not symplectic in the full six-dimensional phase space for relativistic Hamiltonians.
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