dorsal/arxiv
View SchemaNonlinear Dirac equations and nonlinear gauge transformations
| Authors | H. -D. Doebner, R. Zhdanov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0304167 |
| URL | https://arxiv.org/abs/quant-ph/0304167 |
Abstract
Nonlinear Dirac equations (NLDE) are derived through a group N^2 of nonlinear (gauge) transformation acting in the corresponding state space. The construction generalises a construction for nonlinear Schr\"odinger equations. To relate N^2 with physically motivated principles we assume: locality (i.e. it contains no explicit derivative and no derivatives of the wave function), separability (i.e. it acts on product states componentwise) and Poincar\'e invariance. Furthermore we want that a positional density is invariant under N^2. Such nonlinear transformations yield NLDE which describe physically equivalent systems. To get 'new' systems, we extend this NLDE (gauge extension) and present a family of NLDE which is a slight nonlinear generalisation of the Dirac equation. We discuss and comment the fact that nonlinear evolutions are not consistent with the usual framework of quantum theory. To develop a corresponding extended framework one needs models for nonlinear evolutions which also indicate possible physical consequences of nonlinearities.
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"abstract": "Nonlinear Dirac equations (NLDE) are derived through a group N^2 of nonlinear\n(gauge) transformation acting in the corresponding state space. The\nconstruction generalises a construction for nonlinear Schr\\\"odinger equations.\nTo relate N^2 with physically motivated principles we assume: locality (i.e. it\ncontains no explicit derivative and no derivatives of the wave function),\nseparability (i.e. it acts on product states componentwise) and Poincar\\\u0027e\ninvariance. Furthermore we want that a positional density is invariant under\nN^2. Such nonlinear transformations yield NLDE which describe physically\nequivalent systems. To get \u0027new\u0027 systems, we extend this NLDE (gauge extension)\nand present a family of NLDE which is a slight nonlinear generalisation of the\nDirac equation. We discuss and comment the fact that nonlinear evolutions are\nnot consistent with the usual framework of quantum theory. To develop a\ncorresponding extended framework one needs models for nonlinear evolutions\nwhich also indicate possible physical consequences of nonlinearities.",
"arxiv_id": "quant-ph/0304167",
"authors": [
"H. -D. Doebner",
"R. Zhdanov"
],
"categories": [
"quant-ph"
],
"title": "Nonlinear Dirac equations and nonlinear gauge transformations",
"url": "https://arxiv.org/abs/quant-ph/0304167"
},
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