Nambu-type generalization of the Dirac equation

1996/01/16 by Marek Czachor · 26 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Dirac (video compression format) #Dirac algebra #Dirac equation #Generalization #Homotopy and Cohomology in Algebraic Topology #Mathematical analysis #Mathematical physics #Mathematics #Metric (unit) #Nonlinear system #Physics #Poisson distribution #Pure mathematics #Quantum mechanics #Type (biology) #hep-th #quant-ph

paper · pdf · doi:10.1016/s0375-9601(96)00869-9

published in Physics Letters A 225(1-3), 1-12 (Elsevier BV) · revtex, 19 pages

arxiv created 1996/01/16 · openalex publication_date 1997/01/01 · arxiv updated 2014/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Nonlinear generalization of the Dirac equation extending the standard paradigm of nonlinear Hamiltonians is discussed. ``Faster-than-light telegraphs" are absent for all theories formulated within the new framework. A new metric for infinite dimensional Lie algebras associated with Lie-Poisson dynamics is introduced.

Citations

• Theory of Group Representations and Applications
• Nonlinear Schrödinger equation and two-level atoms
• Testing quantum mechanics
• On foundation of the generalized Nambu mechanics

Cited by

• Darboux integration of
• Torsion-Driven Nonlinearity in Spinless Quantum Mechanics
• Vacuum Cherenkov effect in logarithmic nonlinear quantum theory
• Density matrix interpretation of solutions of Lie-Nambu equations
• Complete positivity of nonlinear evolution: A case study