2007/07/31 by Wei-Khim Ng, W. Ng, Rajesh R. Parwani
Mathematics · Physics and Astronomy · #Applied mathematics #Black Holes and Theoretical Physics #Conservation law #Dirac (video compression format) #Dirac algebra #Dirac equation #Geometry #Homogeneous space #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Nonlinear system #Physics #Polynomial #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Relativistic wave equations #Two-body Dirac equations #hep-th #quant-ph
paper · pdf · doi:10.3842/sigma.2009.023
published as SIGMA 5 (2009), 023, 20 pages
arxiv created 2009/02/27 · openalex publication_date 2009/02/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 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.