  The Fock-Hilbert space generated by a single-particle interaction-free
Wightman field is augmented by introducing non-trivial multi-particle (that is,
multi-point, multilinear) quantum fields, which is justified insofar as Haag's
theorem establishes that free field Fock-Hilbert spaces cannot model bound or
interacting states. Two Gaussian constructions are given: one that modifies the
combinatoric factors and masses associated with products of propagators and a
second for which locality is determined by the center of mass of the
n-particles and relative separations of the n-particles determine the strength
of resonance; it is shown how the two constructions may also be used together.
Finally, a method is given for generating non-Gaussian n-particle quantum
fields that quite closely tracks familiar interacting quantum fields but that
is significantly better-defined and that offers a much richer algebraic
structure for future use.
