  Light-pulse atom interferometers rely on the wave nature of matter and its
manipulation with coherent laser pulses. They are used for precise gravimetry
and inertial sensing as well as for accurate measurements of fundamental
constants. Reaching higher precision requires longer interferometer times which
are naturally encountered in microgravity environments such as drop-tower
facilities, sounding rockets and dedicated satellite missions aiming at
fundamental quantum physics in space. In all those cases, it is necessary to
consider arbitrary trajectories and varying orientations of the interferometer
set-up in non-inertial frames of reference.
  Here we provide a versatile representation-free description of atom
interferometry entirely based on operator algebra to address this general
situation. We show how to analytically determine the phase shift as well as the
visibility of interferometers with an arbitrary number of pulses including the
effects of local gravitational accelerations, gravity gradients, the rotation
of the lasers and non-inertial frames of reference. Our method conveniently
unifies previous results and facilitates the investigation of novel
interferometer geometries.
