Of ghosts, gauge volumes, and Gauss's law

The relationship between the canonical operator and the path integral formu lation of quantumelectrodynamics is analyzed with a particular focus on the implementation of auge constraints in the two approaches. The removal of g auge volumes in the path integral is shown to match with the presence of ze ro-norm ghost states associated with gauge transformations in the canonical operator approach. The path integrals for QED in both the Feynman and the temporal gauges are examined and several ways of implementing the gauge con straint integrations are demonstrated. The upshot is to show that both the feynman and the temporal gauge path integrals are equivalent to the coulomb gauge path integral, matching the results developed by Kurt Haller using t he canonical formalism. In addition, the Faddeev-Popov form for the Feynman gauge and temporal gauge Langrangian path integrals are derived from the H amiltonian form of the path integral.