Pair creation and axial anomaly in light-cone $QE{D}_2$

Abstract

The 1+1 dimensional massive Dirac equation is solved exactly in light-cone coordinates for $x^{+}>0$ and $x^{-}>-L$, in the presence of an arbitrary $x^{+}$ dependent electric field. Our solution resolves the ambiguity at $p^{+}=0$. We also obtain the one loop rate for pair production for a positive electric field, compute the expectation values of the vector and axial vector currents, and recover the well known anomaly $e^{2}E/\pi$ in the divergence of the latter. A final intriguing result is that the theory seems to exhibit a phase transition in the limit of infinite $L$.

Comments: 33 pages, 2 figures, LaTeX 2 epsilon, revised for publication