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We have obtained propagators in the position space as an expansion overLandau levels for the charged scalar particle, fermion, and massive vectorboson in a constant external magnetic field. The summation terms in theresulting expressions consisted of two factors, one being rotationallyinvariant in the 2-dimensional Euclidean space perpendicular to the directionof the field, and the other being Lorentz-invariant in the 1+1-dimensionalspace-time. The obtained representations are unique in the sense that theyallow for the simultaneous study of the propagator from both space-time andenergetic perspectives which are implicitly connected. These results contributeto the development of position-space techniques in QFT and are expected to beof use in the calculations of loop diagrams.

Position-space representation of charged particles' propagators in a constant magnetic field as an expansion over Landau levels