Nonlinear Dirac Equations
We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant...
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| Datum: | 2009 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2009
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/149176 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Nonlinear Dirac Equations / Wei Khim Ng, Rajesh R. Parwani // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 46 назв. — англ. |
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irk-123456789-1491762019-02-20T01:26:39Z Nonlinear Dirac Equations Wei Khim Ng Rajesh R. Parwani We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations. 2009 Article Nonlinear Dirac Equations / Wei Khim Ng, Rajesh R. Parwani // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 46 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 81P05; 81Q99; 83A05 http://dspace.nbuv.gov.ua/handle/123456789/149176 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations. |
| format |
Article |
| author |
Wei Khim Ng Rajesh R. Parwani |
| spellingShingle |
Wei Khim Ng Rajesh R. Parwani Nonlinear Dirac Equations Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Wei Khim Ng Rajesh R. Parwani |
| author_sort |
Wei Khim Ng |
| title |
Nonlinear Dirac Equations |
| title_short |
Nonlinear Dirac Equations |
| title_full |
Nonlinear Dirac Equations |
| title_fullStr |
Nonlinear Dirac Equations |
| title_full_unstemmed |
Nonlinear Dirac Equations |
| title_sort |
nonlinear dirac equations |
| publisher |
Інститут математики НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149176 |
| citation_txt |
Nonlinear Dirac Equations / Wei Khim Ng, Rajesh R. Parwani // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 46 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT weikhimng nonlineardiracequations AT rajeshrparwani nonlineardiracequations |
| first_indexed |
2025-07-12T21:34:47Z |
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2025-07-12T21:34:47Z |
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1837478540302352384 |