Comments on the absence of spontaneous symmetry breaking in low dimensions

Abstract

We present some comments intended to bring out simply and more explicitly the physics behind the rigorously proven results on the absence of continuous symmetry breaking in (1 + 1) dimensions at $T=0\mathrm{}$ and (2 + 1) dimensions for $T>\mathrm{}0\mathrm{}$. It is also pointed out within a model that a massless boson is present, in a sense defined in the text, even though symmetry breaking disappears.