On gauge-invariant Green function in 2+1 dimensional QED

الأصل · EN

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 infra-red divergence of gauge-dependent Green function is found to be regulariable, the anomalous dimension is found to be η= 643 π² N. This anomalous dimension was argued to be the same as that of gauge-invariant Green function. However, in Coulomb gauge, the infra-red divergence of the gauge-dependent Green function is found to be un-regulariable, anomalous dimension is even not defined, but the infra-red divergence is shown to be cancelled 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.