Nonlinear Dirac Equations

Details Nonlinear Dirac Equations Nonlinear Dirac Equations

2007-07-11

arxiv.org/abs/0707.1553v2

SIGMA 5 (2009), 023, 20 pages

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

10.3842/SIGMA.2009.023

We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincar\'e 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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