1+1 string with quarks at the ends revisited

The canonical description is presented for the string with pointlike masses at the ends in 1+1 dimensions in two different gauges: in the proper time gauge and in the light-cone one. The classical canonical transformation is written out explicitly, which relates physical variables in both gauges, and the equivalence of the two classical theories is demonstrated in such a way. Both theories are quantized, and it is shown that the quantum theories are not unitary equivalent. This happens due to the fact that the canonical transformation depends on interaction. The quantum Poincaré algebra proves to be closed in both cases, so that the requirement of Poincaré covariance is not able to distinguish between the two versions of the theory.