  Since variational symplectic integrators for the guiding center was proposed
[1,2], structure-preserving geometric algorithms have become an active research
field in plasma physics. We found that the slow manifolds of the classical
Pauli particle enable a family of structure-preserving geometric algorithms for
guiding center dynamics with long-term stability and accuracy. This discovery
overcomes the difficulty associated with the unstable parasitic modes for
variational symplectic integrators when applied to the degenerate guiding
center Lagrangian. It is a pleasant surprise that Pauli's Hamiltonian for
electrons, which predated the Dirac equation and marks the beginning of
particle physics, reappears in classical physics as an effective algorithm for
solving an important plasma physics problem. This technique is applicable to
other degenerate Lagrangians reduced from regular Lagrangians.
