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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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2009
Hauptverfasser: Wei Khim Ng, Rajesh R. Parwani
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2009
Online Zugang:https://nasplib.isofts.kiev.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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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Wei Khim Ng
Rajesh R. Parwani
author_facet Wei Khim Ng
Rajesh R. Parwani
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.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
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.
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-12-07T16:52:12Z
publishDate 2009
publisher Інститут математики НАН України
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spelling Wei Khim Ng
Rajesh R. Parwani
2019-02-19T18:13:18Z
2019-02-19T18:13:18Z
2009
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
https://nasplib.isofts.kiev.ua/handle/123456789/149176
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.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Nonlinear Dirac Equations
Article
published earlier
spellingShingle Nonlinear Dirac Equations
Wei Khim Ng
Rajesh R. Parwani
title Nonlinear Dirac Equations
title_full Nonlinear Dirac Equations
title_fullStr Nonlinear Dirac Equations
title_full_unstemmed Nonlinear Dirac Equations
title_short Nonlinear Dirac Equations
title_sort nonlinear dirac equations
url https://nasplib.isofts.kiev.ua/handle/123456789/149176
work_keys_str_mv AT weikhimng nonlineardiracequations
AT rajeshrparwani nonlineardiracequations