The Gauge Technique in QED_{2+1}

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 \[ S(p)\to \frac{(γ\cdot p+m)}{(p^{2}-m^{2})}(\frac{p^{2}-m^{2}}{% 2m^{2}})^ζ\exp (-\frac{ης}{2}), \] where $ς=e^{2}/(4πm)$ 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 $Φ(z,1,ς)$ explicitly .The vacuum expectation value $< \overlineψψ>$ is gauge dependent . Thus dynamical mass generation does not occur.