Gauge (non-)invariant Green functions of Dirac fermions coupled to gauge fields

About ten years ago the use of standard functional manipulations was demonstrated to imply an unexpected property satisfied by the fermionic Green's functions of QCD and dubbed Effective Locality. This feature of QCD is nonperturbative as it results from a full gauge invariant integration of the gluonic degrees of freedom. In this review article, a few salient theoretical aspects and phenomenological applications of this property are summarized.

About twelve years ago the use of standard functional manipulations was demonstrated to imply an unexpected property satisfied by the fermionic Green's functions of QCD. This non-perturbative phenomenon is dubbed Effective Locality. In a much simpler way than in QCD, the most remarkable and intriguing aspects of Effective Locality have been presented in a recent letter in the Yang-Mills theory on Minkowski spacetime. While quickly recalled in the current paper, these results ...

Accurate calculations of macroscopic and mesoscopic properties in quantum electrodynamics require careful treatment of infrared divergences: standard treatments introduce spurious large-distances effects. A method for computing these properties was developed in a companion paper. That method depends upon a result obtained here about the nature of the singularities that produce the dominant large-distance behaviour. If all particles in a quantum field theory have non-zero mass...

We study in this paper the properties of a gas of fermions coupling to a U(1) gauge field at wavevectors $q<\Lambda<<k_F$ at dimensions larger than one, where $\Lambda<<k_F$ is a high momentum cutoff and $k_F$ is the fermi wave vector. In particular, we shall consider the $e^2\to\infty$ limit where charge and current fluctuations at wave vectors $q<\Lambda$ are forbidden. Within a bosonization approximation, effective actions describing the low energy physics of the system ar...

A procedure for reducing the functional integral of QED to an integral over bosonic gauge invariant fields is presented. Next, a certain averaging method for this integral, giving a tractable effective quantum field theory, is proposed. Finally, the current-current propagator and the chiral anomaly are calculated within this new formulation. These results are part of our programme of analyzing gauge theories with fermions in terms of local gauge invariants.

In a recent preprint [cond-mat/0204040] Khveshchenko questioned the validity of our computation of the gauge invariant fermion propagator in QED3, which we employed as an effective theory of high-T_c cuprate superconductors [cond-mat/0203333]. We take this opportunity to further clarify our procedure and to show that criticism voiced in the above preprint is unwarranted.

Quantum field theory is assumed to be gauge invariant. However it is well known that when certain quantities are calculated using perturbation theory the results are not gauge invariant. The non-gauge invariant terms have to be removed in order to obtain a physically correct result. In this paper we will examine this problem and determine why a theory that is supposed to be gauge invariant produces non-gauge invariant results.

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, o...

By applying the simple and effective method developed to study the the gauge-invariant fermion Green function in $ 2+1 $ dimensional non-compact QED, we study the gauge-invariant Green function in $ 3+1 $ dimensional QED and $ 2+1 $ dimensional non-compact Chern-Simon theory. We also extend our results to the corresponding $ SU(M) $ non-Abelian gauge theories. Implications for Fractional Quantum Hall effect are briefly discussed.

We show that the gauge-fermion interaction in multiflavour $(2+1)$-dimensional quantum electrodynamics with a finite infrared cut-off is responsible for non-fermi liquid behaviour in the infrared, in the sense of leading to the existence of a non-trivial fixed point at zero momentum, as well as to a significant slowing down of the running of the coupling at intermediate scales as compared with previous analyses on the subject. Both these features constitute deviations from fe...