Quantum field dynamics in a uniform magnetic field: Description using fields in oblique phase space

We present a simple field transformation that changes the field arguments from ordinary position-space coordinates to oblique phase-space coordinates that are linear in position and momentum variables. This is useful in studying quantum field dynamics in the presence of an 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 a 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.