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

Jinwu Ye
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Abstract

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= \frac{64}{3 π^{2} 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.

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Jinwu Ye. 2003-01-04. On gauge-invariant Green function in 2+1 dimensional QED. https://doi.org/10.1103/physrevb.67.115104

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