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

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 $\eta =\frac{64}{3{\pi }^{2}N}$. 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.

8 pages, 6 figures, to appear in Phys. Rev. B

References in corpus (2)

• Thermally generated vortices, gauge invariance and electron spectral function in the pseudo-gap regime
• Quantum generated vortices, dual singular gauge transformation and zero temperature transition from d-wave superconductor to underdoped regime

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