2005/12/22 by Peter Morgan, Morgan, Peter
Physics and Astronomy · #FOS: Physical sciences #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0512190
10 pages. v2: relationship of the method to renormalization outlined
openalex publication_date 2005/12/22 · arxiv created 2006/10/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
There are still no interacting models of the Wightman axioms, suggesting that the axioms are too tightly drawn. Here a weakening of linearity for quantum fields is proposed, with the algebra still linear but with the quantum fields no longer required to be tempered distributions, allowing explicit interacting quantum field models. Interacting quantum fields should be understood to be nonlinear quantum fields in this sense, because a set of effective field theories encodes a dependence on the energy scale of measurement -- which is a nontrivial property of the test functions -- so that correlation functions are implicitly nonlinear functions of test functions in the conventional formalism. In Local Quantum Physics terms, the algebraic models constructed here do not satisfy the additivity property. Finite nonlinear deformations of quantized electromagnetism are constructed as examples.