dorsal/arxiv
View SchemaStructure of nonlinear gauge transformations
| Authors | Marek Czachor |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9711053 |
| URL | https://arxiv.org/abs/quant-ph/9711053 |
| DOI | 10.1103/PhysRevA.57.R2263 |
| Journal | Phys.Rev. A57 (1998) 2263 |
Abstract
Nonlinear Doebner-Goldin [Phys. Rev. A 54, 3764 (1996)] gauge transformations (NGT) defined in terms of a wave function $\psi(x)$ do not form a group. To get a group property one has to consider transformations that act differently on different branches of the complex argument function and the knowledge of the value of $\psi(x)$ is not sufficient for a well defined NGT. NGT that are well defined in terms of $\psi(x)$ form a semigroup parametrized by a real number $\gamma$ and a nonzero $\lambda$ which is either an integer or $-1\leq \lambda\leq 1$. An extension of NGT to projectors and general density matrices leads to NGT with complex $\gamma$. Both linearity of evolution and Hermiticity of density matrices are gauge dependent properties.
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"abstract": "Nonlinear Doebner-Goldin [Phys. Rev. A 54, 3764 (1996)] gauge transformations\n(NGT) defined in terms of a wave function $\\psi(x)$ do not form a group. To get\na group property one has to consider transformations that act differently on\ndifferent branches of the complex argument function and the knowledge of the\nvalue of $\\psi(x)$ is not sufficient for a well defined NGT. NGT that are well\ndefined in terms of $\\psi(x)$ form a semigroup parametrized by a real number\n$\\gamma$ and a nonzero $\\lambda$ which is either an integer or $-1\\leq\n\\lambda\\leq 1$. An extension of NGT to projectors and general density matrices\nleads to NGT with complex $\\gamma$. Both linearity of evolution and Hermiticity\nof density matrices are gauge dependent properties.",
"arxiv_id": "quant-ph/9711053",
"authors": [
"Marek Czachor"
],
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"quant-ph"
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"doi": "10.1103/PhysRevA.57.R2263",
"journal_ref": "Phys.Rev. A57 (1998) 2263",
"title": "Structure of nonlinear gauge transformations",
"url": "https://arxiv.org/abs/quant-ph/9711053"
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