Please use this identifier to cite or link to this item: https://doi.org/10.3842/SIGMA.2009.023
Title: Nonlinear Dirac equations
Authors: Ng, W.K.
Parwani, R.R. 
Keywords: Lorentz violation
Nonlinear Dirac equation
Issue Date: 2009
Citation: Ng, W.K., Parwani, R.R. (2009). Nonlinear Dirac equations. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 5 : -. ScholarBank@NUS Repository. https://doi.org/10.3842/SIGMA.2009.023
Abstract: 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.
Source Title: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
URI: http://scholarbank.nus.edu.sg/handle/10635/97341
ISSN: 18150659
DOI: 10.3842/SIGMA.2009.023
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