Infinite dimensional Lie algebras and current algebra

  • Robert Hermann
Part of the Lecture Notes in Physics book series (LNP, volume 6)


The “current algebras” of elementary particle physics and quantum field theory are interpreted as infinite dimensional Lie algebras of a certain definite kind. The possibilities of algebraic structure and certain types of representations of these algebras by differential operators on manifolds are investigated, in a tentative way. The Sugawara model is used as a typical example. A general differential geometric method (involving jet spaces) for defining currents associated with classical field theories is presented. In connection with the abstract definition of current algebras as modules, a purely module-theoretic definition of a “differential operator” is presented and its properties are studied.


Differential Operator Vector Bundle Commutation Relation Jacobi Identity Current Algebra 
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Copyright information

© Springer-Verlag 1970

Authors and Affiliations

  • Robert Hermann
    • 1
  1. 1.Institute for Advanced StudyPrinceton

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