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Elusive gauge-invariant fermion propagator in QED-like effective theories: round II

D. V. Khveshchenko
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Abstract

We comment on the recent attempt by M. Franz et al [1] to further justify their earlier calculation of the gauge-invariant electron propagator in the context of the QED_3 theory of the pseudogap phase in cuprates [2]. First, we use the method of "reductio ad absurdum" to demonstrate the inconsistency of the argument offered in [2] and then present a direct calculation of the disputed fermion amplitudes, thus unequivocally proving that the previously proposed form of the electron propagator: 1) does exhibit a negative anomalous dimension, as pointed out in [3]; 2) is different from the so-called Brown's function whose anomalous dimension turns out to be positive when computed in a covariant gauge. Lastly, we conjecture that the true physical electron propagator (whose exact form still remains to be found) may feature a "super-Luttinger" behavior characterized by a faster than a power-law decay G(x)~exp(-const\ln^2|x|).

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D. V. Khveshchenko. 2002-05-07. Elusive gauge-invariant fermion propagator in QED-like effective theories: round II. https://arxiv.org/abs/cond-mat/0205106

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