Nonlinear group representations and the linearizability of nonlinear equations

  • Daniel Sternheimer
Gauge Theory Session Organized by A. Trautman
Part of the Lecture Notes in Physics book series (LNP, volume 116)


Basic definitions and some results in the recently developed theory of nonlinear Lie group representations in Banach and Fréchet spaces are presented. Using cohomological methods, this framework permits a study of the linearizability of covariant nonlinear evolution equations. Formal linearizability is proved under some conditions on the linear part of the representation, for massive and for massless Poincaré covariant equations. In particular, pure Yang-Mills equations supplemented with a relativistic gauge condition are formally linearizable.


Formal Series Classical Phase Space General Coordinate Transformation Fr4chet Space Cohomological Method 
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Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Daniel Sternheimer
    • 1
  1. 1.C.N.R.S. Paris and Physique MathématiqueUniversité de DijonFrance

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