Multi-particle quantum fields for bound states and interactions

Peter Morgan

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arXiv · 1507.08299

Multi-particle quantum fields for bound states and interactions

Peter Morgan

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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.

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Peter Morgan. 2015-07-29. Multi-particle quantum fields for bound states and interactions. https://arxiv.org/abs/1507.08299

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