Spontaneous breakdown in two dimensional space-time

We prove that in two-dimensional space-time, symmetry transformations which are generated by Poincaré covariant currents can not be spontaneously broken. This is also the case with the dilation current. We argue that other currents which involve explicit space-time dependence might lead to spontaneously broken symmetries accompanied by massless Goldstone bosons. We construct a trivial example where this phenomenon occurs.