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Pair creation and axial anomaly in light-cone $QED_2$

T. N. Tomaras·N. C. Tsamis·R. P. Woodard
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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 $e^2 E/π$ 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 $L$.

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T. N. Tomaras, N. C. Tsamis, R. P. Woodard. 2001-11-07. Pair creation and axial anomaly in light-cone $QED_2$. https://doi.org/10.1088/1126-6708%2F2001%2F11%2F008

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