Gauge-invariant Green function in 2+1 dimensional quantum electrodynamics

Both the gauge-invariant fermion Green function and gauge-dependent conventional Green function in 2+1-dimensional QED are studied in the large N limit. In temporal gauge, the infrared divergence of the gauge-dependent Green function is found to be regularizable, and the anomalous dimension is found to be η=64/3π²N. This anomalous dimension was argued to be the same as that of the gauge-invariant Green function. However, in Coulomb gauge, the infrared divergence of the gauge-dependent Green function is found to be unregularizable, and the anomalous dimension is not even defined, but the infrared divergence is shown to be canceled in any gauge-invariant physical quantities. The gauge-invariant Green function is also studied directly in Lorentz covariant gauge and the anomalous dimension is found to be the same as that calculated in temporal gauge.