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

Multi-particle quantum fields for bound states and interactions