Formal Breakdown of Lorentz Invariance in Two-Dimensional Field Theories

Abstract

Since the field theory which describes the interaction of a massless fermion with a vector meson of bare mass ${\ensuremath{\mu}}_{0}$ in one spatial dimension is known to contain massless boson excitations, there is considerable interest associated with the question of whether these particles can be identified as the Goldstone bosons generated by the breaking of an appropriate symmetry operation of the theory. It is shown that such an interpretation is indeed consistent, independent of the strength of the coupling, provided that one takes Lorentz invariance to be the broken symmetry of the model. Particular attention is given to the limits ${\ensuremath{\mu}}_{0}\ensuremath{\rightarrow}\ensuremath{\infty}$ (Thirring model) and ${\ensuremath{\mu}}_{0}\ensuremath{\rightarrow}0$ (Schwinger model). It is found in all cases that despite the apparent breaking of Lorentz invariance, the excitation specrtum has a normal form, and the symmetry breakdown remains entirely unobservable.