From generalized Clifford algebras to Nambu's formulation of dynamics
type: Item
instance of: scholarly article
title: From generalized Clifford algebras to Nambu's formulation of dynamics
zbMATH Open document ID: 0973.15023
DOI: 10.1007/BF03042006
author: R. M. Yamaleev
published in: Advances in Applied Clifford Algebras
publication date: 2001-11-25T00:00:00Z
review text: 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.
reviewed by: Jürgen Tolksdorf
Mathematics Subject Classification ID: 15A66
Mathematics Subject Classification ID: 37J05
Mathematics Subject Classification ID: 70H05
zbMATH DE Number: 1568592
zbMATH Keywords: generalized Clifford algebras
zbMATH Keywords: multicomplex algebra
zbMATH Keywords: Hamilton-Nambu dynamical systems
zbMATH Keywords: Hamiltonian
MaRDI profile type: Publication
cites work: Q4356227
cites work: Generalized Clifford algebras and hyperspin manifolds
cites work: Generalized Hamiltonian Dynamics
cites work: Generalized Newtonian equations of motion
cites work: Extended complex number analysis and conformal-like transformations
cites work: Q3249645
cites work: Complex Coordinates and Quantum Mechanics
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description: scientific article; zbMATH DE number 1568592