  We explain, in the first quantized path integral formalism, the mechanism
behind the Anderson-Higgs effect for a gas of charged bosons in a background
magnetic field, and then use the method to prove the absence of the effect for
a gas of fermions. The exchange statistics are encoded via the inclusion of
additional Grassmann coordinates in a manner that leads to a manifest worldline
supersymmetry. This extra symmetry is key in demonstrating the absence of the
effect for charged fermions.
