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Parwani R., Nonlinear Dirac equations

By Wei-khim Ng and Rajesh R. Parwani

Abstract

We study 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, plane wave solutions, modified dispersion relations and the non-relativistic limit. Motivated by some previously suggested applications such as neutrino oscillations, we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples together with their associated properties. We contrast our construction procedure and results with others in the literature and also outline various physical applications we envisage fo

Year: 2012
OAI identifier: oai:CiteSeerX.psu:10.1.1.246.5560
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