  We have obtained propagators in the position space as an expansion over
Landau levels for the charged scalar particle, fermion, and massive vector
boson in a constant external magnetic field. The summation terms in the
resulting expressions consisted of two factors, one being rotationally
invariant in the 2-dimensional Euclidean space perpendicular to the direction
of the field, and the other being Lorentz-invariant in the 1+1-dimensional
space-time. The obtained representations are unique in the sense that they
allow for the simultaneous study of the propagator from both space-time and
energetic perspectives which are implicitly connected. These results contribute
to the development of position-space techniques in QFT and are expected to be
of use in the calculations of loop diagrams.
