  A particle-in-cell algorithm is derived with a canonical Poisson structure in
the formalism of finite element exterior calculus. The resulting method belongs
to the class of gauge-compatible splitting algorithms, which exactly preserve
gauge symmetries and their associated conservation laws via the momentum map.
We numerically demonstrate this time invariance of the momentum map and its
usefulness in establishing precise initial conditions with a desired initial
electric field and fixed background charge. The restriction of this canonical,
finite element Poisson structure to the 1X2P phase space is also considered and
simulated numerically.
