From generalized Clifford algebras to Nambu's formulation of dynamics
The algebra of multicomplex numbers is used to construct an oscillator model for Nambu's formulation of dynamics in high dimensional phase space. It is shown how Nambu's formalism can be expressed in terms of polylinear metric forms. From this point of view multicomplex algebra, considered as the commutative part of generalized Clifford algebras, is related to the Hamilton-Nambu equations like the algebra of complex numbers is related to Hamilton's equations in two-dimensional phase space. The author proposes a new dynamical principle. From this principle he derives two kinds of Hamilton-Nambu equations in \(d\leq 2\)-dimensional phase space. One of them is determined by one Hamiltonian and \((d-1)\) evolution parameters. In this way the oscillator model is given by homogeneous forms of degree \(d\). In the second formulation the evolution of the dynamical system is generated by (\(d-1\)) Hamiltonians with a single evolution parameter.
scientific article; zbMATH DE number 1568592
scientific article