The authors study the role of (1,1) graded tensor field T in the analysis of complete integrability of dynamical systems with fermionic variables. They find that such a tensor T can be a recursion operator if and only if T is even as a graded map, namely, if and only if p(T)=0. They clarify this fact by constructing an odd tensor for two examples, a supersymmetric Toda chain and a supersymmetric harmonic oscillator. They explicitly show that it cannot be a recursion operator since it does not allow new constants of motion to be built from the first two, in contrast to what usually happens with ordinary, i.e. nongraded systems.
Remarks on the Complete Integrability of Dynamical Systems con Fermionic Variables
MARMO, Giuseppe;VILASI, Gaetano
1992-01-01
Abstract
The authors study the role of (1,1) graded tensor field T in the analysis of complete integrability of dynamical systems with fermionic variables. They find that such a tensor T can be a recursion operator if and only if T is even as a graded map, namely, if and only if p(T)=0. They clarify this fact by constructing an odd tensor for two examples, a supersymmetric Toda chain and a supersymmetric harmonic oscillator. They explicitly show that it cannot be a recursion operator since it does not allow new constants of motion to be built from the first two, in contrast to what usually happens with ordinary, i.e. nongraded systems.File in questo prodotto:
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