Finite Euler Hierarchies And Integrable Universal Equations

Details Finite Euler Hierarchies And Integrable Universal Equations Finite Euler Hierarchies And Integrable Universal Equations

1992-07-13

arxiv.org/abs/hep-th/9207036v2

Czech.J.Phys. 42 (1992) 1313-1324

Physics

High Energy Physics

High Energy Physics - Theory

(replaces previous unprintable version corrupted mailer) 13 p., (Plain TeX), DTP-92/35

Scientific paper

10.1007/BF01589661

Recent work on Euler hierarchies of field theory Lagrangians iteratively constructed {}from their successive equations of motion is briefly reviewed. On the one hand, a certain triality structure is described, relating arbitrary field theories, {\it classical\ts} topological field theories -- whose classical solutions span topological classes of manifolds -- and reparametrisation invariant theories -- generalising ordinary string and membrane theories. On the other hand, {\it finite} Euler hierarchies are constructed for all three classes of theories. These hierarchies terminate with {\it universal\ts} equations of motion, probably defining new integrable systems as they admit an infinity of Lagrangians. Speculations as to the possible relevance of these theories to quantum gravity are also suggested.

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