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Dynamical Chiral Symmetry Breaking in Unquenched ${QED}_3$

C. S. Fischer·R. Alkofer·T. Dahm·P. Maris
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Abstract

We investigate dynamical chiral symmetry breaking in unquenched ${QED}_3$ using the coupled set of Dyson--Schwinger equations for the fermion and photon propagators. For the fermion-photon interaction we employ an ansatz which satisfies its Ward--Green--Takahashi identity. We present self-consistent analytical solutions in the infrared as well as numerical results for all momenta. In Landau gauge, we find a phase transition at a critical number of flavours of $N_f^{\mathrm crit} \approx 4$. In the chirally symmetric phase the infrared behaviour of the propagators is described by power laws with interrelated exponents. For $N_f=1$ and $N_f=2$ we find small values for the chiral condensate in accordance with bounds from recent lattice calculations. We investigate the Dyson--Schwinger equations in other linear covariant gauges as well. A comparison of their solutions to the accordingly transformed Landau gauge solutions shows that the quenched solutions are approximately gauge covariant, but reveals a significant amount of violation of gauge covariance for the unquenched solutions.

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C. S. Fischer, R. Alkofer, T. Dahm, P. Maris. 2004-09-02. Dynamical Chiral Symmetry Breaking in Unquenched ${QED}_3$. https://doi.org/10.1103/physrevd.70.073007

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