The Gauge Technique in QED_{2+1}

TL;DR

This paper applies the Gauge Technique to QED in 2+1 dimensions, analyzing fermion propagators and spectral functions, and concludes that dynamical mass generation does not occur, with results being gauge invariant except for an exponential factor.

Contribution

The study extends the Gauge Technique to QED_{2+1} with infrared subtraction, providing explicit expressions for propagators and spectral functions, and clarifies gauge dependence of the vacuum expectation value.

Findings

Fermion propagator near threshold exhibits gauge-invariant behavior except for an exponential factor.

Spectral functions are explicitly derived in Landau and Yennie-like gauges.

Dynamical mass generation is ruled out due to gauge dependence of <ψ̄ψ>.

Abstract

The Gauge Technique has been applied to QED$_{2+1}$ in the quenched case with infrared subtraction. The behaviour of the fermion propagator near the threshold is then found to be \[ S(p)\to \frac{(\gamma \cdot p+m)}{(p^{2}-m^{2})}(\frac{p^{2}-m^{2}}{% 2m^{2}})^{\zeta}\exp (-\frac{\eta \varsigma}{2}), \] where $\varsigma =e^{2}/(4\pi m)$ and this is gauge invariant except the exponential factor. We also find a spectral function in the Landau and Yennie like gauge. The propagators $S(p)$ are expressed in terms of $\Phi (z,1,\varsigma)$ explicitly .The vacuum expectation value $< \overline{\psi}\psi >$ is gauge dependent . Thus dynamical mass generation does not occur.