dorsal/arxiv
View SchemaFrom time inversion to nonlinear QED
| Authors | Wei Min Jin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0001029 |
| URL | https://arxiv.org/abs/quant-ph/0001029 |
| Journal | Found.Phys. 30 (2000) 1943-1973 |
Abstract
In Minkowski flat space-time, it is perceived that time inversion is unitary rather than antiunitary, with energy being a time vector changing sign under time inversion. The Dirac equation, in the case of electromagnetic interaction, is not invariant under unitary time inversion, giving rise to a ``Klein paradox''. To render unitary time inversion invariance, a nonlinear wave equation is constructed, in which the ``Klein paradox'' disappears. In the case of Coulomb interaction, the revised nonlinear equation can be linearized to give energy solutions for Hydrogen-like ions without singularity when nuclear number $Z>137$, showing a reversed energy order pending for experimental tests such as Zeeman effects. In non-relativistic limit, this nonlinear equation reduces to nonlinear schr\"odinger equation with soliton-like solutions. Moreover, particle conjugation and electron-proton scattering with a nonsingular current-potential interaction are discussed. Finally the explicit form of gauge function is found, the uniqueness of Lorentz gauge is proven and the Lagrangian density of quantum electrodynamics (QED) is revised as well. The implementation of unitary time inversion leads to the ultimate derivation of nonlinear QED.
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"abstract": "In Minkowski flat space-time, it is perceived that time inversion is unitary\nrather than antiunitary, with energy being a time vector changing sign under\ntime inversion. The Dirac equation, in the case of electromagnetic interaction,\nis not invariant under unitary time inversion, giving rise to a ``Klein\nparadox\u0027\u0027. To render unitary time inversion invariance, a nonlinear wave\nequation is constructed, in which the ``Klein paradox\u0027\u0027 disappears. In the case\nof Coulomb interaction, the revised nonlinear equation can be linearized to\ngive energy solutions for Hydrogen-like ions without singularity when nuclear\nnumber $Z\u003e137$, showing a reversed energy order pending for experimental tests\nsuch as Zeeman effects. In non-relativistic limit, this nonlinear equation\nreduces to nonlinear schr\\\"odinger equation with soliton-like solutions.\nMoreover, particle conjugation and electron-proton scattering with a\nnonsingular current-potential interaction are discussed. Finally the explicit\nform of gauge function is found, the uniqueness of Lorentz gauge is proven and\nthe Lagrangian density of quantum electrodynamics (QED) is revised as well. The\nimplementation of unitary time inversion leads to the ultimate derivation of\nnonlinear QED.",
"arxiv_id": "quant-ph/0001029",
"authors": [
"Wei Min Jin"
],
"categories": [
"quant-ph",
"gr-qc",
"hep-th",
"nlin.PS",
"physics.atom-ph"
],
"journal_ref": "Found.Phys. 30 (2000) 1943-1973",
"title": "From time inversion to nonlinear QED",
"url": "https://arxiv.org/abs/quant-ph/0001029"
},
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