Nonlinear Dirac equations and nonlinear gauge transformations
| dc.creator | Doebner, H. -D. | |
| dc.creator | Zhdanov, R. | |
| dc.date | 2003-04-25 | |
| dc.date.accessioned | 2026-07-07T06:06:38Z | |
| dc.date.available | 2026-07-07T06:06:38Z | |
| dc.description | 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 Schrödinger 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 Poincaré 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. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0304167 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0304167 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/91046 | |
| dc.subject | Quantum Physics | |
| dc.title | Nonlinear Dirac equations and nonlinear gauge transformations | |
| dc.type | text |