Dimensional regularization of gauge theories in spherical spacetime: Free field trace anomalies

The O(n + 1) covariant formulation of massless quantum electrodynamics in spherical spacetime is further developed to allow a calculation of the energy-momentum tensor trace anomalies for the free Dirac, electromagnetic, and SU(2) gauge fields. The principal technical development is the construction of the Faddeev-Popov ghosts for electrodynamics and SU(2) Yang-Mills theory. This construction is unconventional first in that the gauge fixing term in the Lagrangian is not a perfect square, and second because it is necessary to remove radial as well as gauge degrees of freedom from the measure of the functional integral. The ghost fields are shown to satisfy a minimal scalar field equation. The free field effective action is found to be divergent in four dimensions, and is renormalized by the inclusion in the Lagrangian of a counterterm local in the gravitational fields. The energy-momentum tensor calculated from this renormalized effective action is shown to have a trace anomaly.