One-particle propagators for rational values of the filling factor and their fractionally charged excitations

Free electron propagators for the 2D-electron gas in a magnetic field are presented. They describe translationally invariant ground states for arbitrary values of the filling factor υ=p/q ≤1 with q and p integers. The magnetic translation group Ward identities are also satisfied by them. For each rational value of the filling factor there exist a family of related propagators. All the members have the same properties far away from the origin, but show localized charge excitations having rational fractions of the electron charge. For υ=1/q with q odd, zero charged distributions exist. When q is even all the configurations are charged. Exact free electron propagators corresponding with crystalline states are constructed by using the magnetic translational invariance, for the odd q values. It seems not ruled out that these states may correspond with stable FQHE wave functions spontaneously breaking the magnetic translational invariance. (author). 13 refs