Poisson Hierarchy of Discrete Strings

Abstract

The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equa- tion is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra.

References in corpus (2)

• On spinors, strings, integrable models and decomposed Yang-Mills theory
• Gauge field, strings, solitons, anomalies and the speed of life

Cited by in corpus (4)

• Chern-Simons Improved Hamiltonians for Strings in Three Space Dimensions
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• Solution X-ray scattering (S/WAXS) and structure formation in protein dynamics
• On relation between discrete Frenet frames and the bi-Hamiltonian structure of the discrete nonlinear Schrödinger equation