Example of a Poincare anomaly in relativistic quantum mechanics

The Poincare algebra of classical electrodynamics in one spatial dimension is studied using light-cone coordinates and ordinary Minkowski coordinates. We show that it is possible to quantize the theory by a canonical quantization procedure in a Poincare invariant manner on the light-cone. We also show that this is not possible when using ordinary coordinates. The physical reason of this anomaly is analysed.