  Since the late 1950's, the dynamics of a charged particle's ``guiding center"
in a strong, inhomogeneous magnetic field have been understood in terms of
near-identity coordinate transformations. The basic idea has been to
approximately transform away the coupling between the fast gyration around
magnetic fields lines and the remaining slow dynamics. This basic understanding
now serves as a foundation for describing the kinetic theory of strongly
magnetized plasmas. I present a new way to understand guiding center dynamics
that does not involve complicated coordinate transformations. Starting from a
dynamical systems formulation of the motion of parameterized loops in a charged
particle's phase space, I identify a formal slow manifold in loop space.
Dynamics on this formal slow manifold are equivalent to guiding center dynamics
to all orders in perturbation theory. After demonstrating that loop space
dynamics comprises an infinite-dimensional noncanonical Hamiltonian system, I
recover the well-known Hamiltonian formulation of guiding center motion by
restricting the (pre-) symplectic structure on loop space to the
finite-dimensional guiding center formal slow manifold.
