Anomalous dimensions of gauge-invariant amplitudes in massless effective gauge theories of strongly correlated systems

TL;DR

This paper calculates the anomalous dimensions of gauge-invariant electron propagators in effective gauge theories of strongly correlated systems, clarifying previous disputes and laying groundwork for further physical predictions.

Contribution

It introduces a calculation of the anomalous dimension using the radial gauge in $QED_3$ models, resolving prior disagreements about its sign and magnitude.

Findings

Confirmed the sign and magnitude of the anomalous dimension

Clarified the gauge-invariant amplitude behavior

Established a basis for future physical amplitude computations

Abstract

We use the radial gauge to calculate the recently proposed ansatz for the physical electron propagator in such effective models of strongly correlated electron systems as the $QED_3$ theory of the pseudogap phase of the cuprates. The results of our analysis help to settle the recent dispute about the sign and the magnitude of the anomalous dimension which characterizes the gauge invariant amplitude in question and set the stage for computing other, more physically relevant, ones.