Weakened linearity for quantum fields

Details Weakened linearity for quantum fields Weakened linearity for quantum fields

2005-12-22

arxiv.org/abs/quant-ph/0512190v2

Physics

Quantum Physics

10 pages. v2: relationship of the method to renormalization outlined

Scientific paper

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.

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