We d iscuss the possibility of constructing out of par title creation and destruction operators local quantum fields which transform as representations of the homogeneous Lorentz group. Our immediate goal is to write down a consistent local quantum field theory which can simultaneously describe many particles with different masses and spins. In the case that the field is a finite dimensional irreducible Iorentz tensor, we are able to carry through our program with no restrictions on the masses considered as functions of the spin, provided the usual connection between spin and statistics is satisfied. However, when the field transforms as a unitary irreducible representation of the homogeneous Lorentz group (an infinite dimensional representation), the requirement of locality, along with the physical assumption that the masses are bounded below
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