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 \[ S(p)\to \frac{(\gamma \cdot p+m)}{(p^{2}-m^{2})}(\frac{p^{2}-m^{2}}{% 2m^{2}})^{\zeta}\exp (-\frac{\eta \varsigma}{2}), \] 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.