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

TL;DR

This paper critically examines the gauge-invariant electron propagator in QED_3 theories related to cuprates, demonstrating inconsistencies in previous calculations and proposing that the true propagator may decay faster than any power law.

Contribution

It provides a direct calculation showing the incorrectness of earlier proposals and suggests a novel super-Luttinger decay form for the physical electron propagator.

Findings

Previous propagator form has negative anomalous dimension

Disputed propagator differs from Brown's function with positive anomalous dimension

Conjecture of a super-Luttinger decay faster than power-law

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|).