  A class of free quantum fields defined on the Poincare' group, is described
by means of their two-point vacuum expectation values. They are not equivalent
to fields defined on the Minkowski spacetime and they are "elementary" in the
sense that they describe particles that transform according to irreducible
unitary representations of the symmetry group, 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 describe particles with positive mass and arbitrary
spin and particles with zero mass and arbitrary helicity or with an infinite
helicity spectrum. In each case the allowed SL(2, C) internal quantum numbers
are specified. The properties of local commutativity and the limit in which one
recovers the usual field theories in Minkowski spacetime are discussed. By
means of a superposition of elementary fields, one obtains an example of a
field that present a broken symmetry with respect to the group Sp(4, R), that
survives in the short-distance limit. Finally, the interaction with an
accelerated external source is studied and 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 finite critical value.
