NONRELATIVISTIC CONFORMAL GROUPS .2. FURTHER DEVELOPMENTS AND PHYSICAL APPLICATIONS

The finite-dimensional conformal groups associated with the Galilei an d (oscillating or expanding) Newton-Hooke space-time manifolds was cha racterized by the present authors in a recent work. Three isomorphic g roup families, one for each nonrelativistic kinematics, were obtained, whose members are labeled by a half-integer number l. Since the actio n of these groups on their corresponding space-time manifolds is only local, a linearization is introduced here such that the corresponding action is well defined everywhere. In particular, the (I=1)-conformal cases that can be obtained by contraction from the well-known Minkowsk ian conformal group are treated in more detail. As an application of p hysical interest, the conformal invariance of the Galilean electromagn etism is studied. In order to achieve it? the pertinent local represen tations of the Galilean conformal algebras are derived. (C) 1997 Ameri can Institute of Physics.