dorsal/arxiv
View SchemaWeakened linearity for quantum fields
| Authors | Peter Morgan |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0512190 |
| URL | https://arxiv.org/abs/quant-ph/0512190 |
Abstract
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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"abstract": "There are still no interacting models of the Wightman axioms, suggesting that\nthe axioms are too tightly drawn. Here a weakening of linearity for quantum\nfields is proposed, with the algebra still linear but with the quantum fields\nno longer required to be tempered distributions, allowing explicit interacting\nquantum field models. Interacting quantum fields should be understood to be\nnonlinear quantum fields in this sense, because a set of effective field\ntheories encodes a dependence on the energy scale of measurement -- which is a\nnontrivial property of the test functions -- so that correlation functions are\nimplicitly nonlinear functions of test functions in the conventional formalism.\nIn Local Quantum Physics terms, the algebraic models constructed here do not\nsatisfy the additivity property. Finite nonlinear deformations of quantized\nelectromagnetism are constructed as examples.",
"arxiv_id": "quant-ph/0512190",
"authors": [
"Peter Morgan"
],
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"title": "Weakened linearity for quantum fields",
"url": "https://arxiv.org/abs/quant-ph/0512190"
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