Multi-particle quantum fields for bound states and interactions

Abstract

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.