FREE QUANTUM-FIELDS ON THE POINCARE GROUP

A class of free quantum fields defined on the Poincare group is descri bed by means of their two-point vacuum expectation values. They are no t equivalent to fields defined on the Minkowski space-time and they ar e ''elementary'' in the sense that they describe particles that transf orm according to irreducible unitary representations of the symmetry g roup, given by the product of the Poincare group and of the group SL(2 ,C) considered as an internal symmetry group. Some of these fields des cribe particles with positive mass and arbitrary spin and particles wi th zero mass and arbitrary helicity or with an infinite helicity spect rum. In each case the allowed SL(2,C) internal quantum numbers are spe cified. The properties of local commutativity and the limit in which o ne recovers the usual field theories in Minkowski space-time are discu ssed. By means of a superposition of elementary fields, one obtains an example of a field that presents a broken symmetry with respect to th e group Sp(4,R) that survives in the short-distance limit. Finally, th e interaction with an accelerated external source is studied and it is shown that, in some theories, the average number of particles emitted per unit of proper time diverges when the acceleration exceeds a fini te critical value. (C) 1996 American Institute of Physics.