  Sums of walks for charged particles (e.g. Hofstadter electrons) on a square
lattice in the presence of a magnetic field are evaluated. Returning loops are
systematically added to directed paths to obtain the unrestricted propagators.
Expressions are obtained for special values of the magnetic flux-per-plaquette
commensurate with the flux quantum. For commensurate and incommensurate values
of the flux, the addition of small returning loops does not affect the general
features found earlier for directed paths. Lattice Green's functions are also
obtained for staggered flux configurations encountered in models of high-Tc
superconductors.
