  We present a simple field transformation which changes the field arguments
from the ordinary position-space coordinates to the oblique phase-space
coordinates that are linear in position and momentum variables. This is useful
in studying quantum field dynamics in the presence of external uniform magnetic
field: here, the field transformation serves to separate the dynamics within
the given Landau level from that between different Landau levels. We apply this
formalism to both nonrelativistic and relativistic field theories. In the large
external magnetic field our formalism provides an efficient method for
constructing the relevant lower-dimensional effective field theories with the
field degrees defined only on the lowest Landau level.
