ar X iv : h ep - t h / 01 02 19 1 v 2 1 F eb 2 00 2 Wigner ’ s Little Group , Gauge Transformations and Dimensional Descent

Wigner’s little group[1], which is a subgroup of the Poincare group that leaves the fourmomentum invariant, is of fundamental importance for both massive and massless particles. In the latter case this group is E(2), which is a semi-direct product of T (2) (the group of translations in the plane) and SO(2). Each of these subgroups has its own role, but here we are concerned with T (2) which acts as a generator of gauge transformation[2, 3] in usual gauge theories, like Maxwell or Kalb-Ramond[4], where the quanta of excitations are massless. There are however instances where gauge invariance coexists with mass the topologically massive gauge theories like the B ∧ F [5] theory or the Maxwell-Chern-Simons(MCS)[6] theory in 2+1 dimensions. Recently we had shown[7] that in the B∧F theory, the gauge invariance is generated by a particular representation of T (3) ⊂ E(3), so that one has to go beyond Wigner’s little group. For the MCS model, however, Wigner’s little group (isomorphic to R×Z2) itself suffices, albeit in a different representation. Is there then a systematic method of obtaining these distinct representations and, if possible, connect them to Wigner’s little group for massless particles, which acts as gauge generator for conventional gauge theories?