Poisson Hierarchy of Discrete Strings
High Energy Physics - Theory
2016-01-20 v1 Statistical Mechanics
High Energy Physics - Lattice
Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
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.
Cite
@article{arxiv.1507.05792,
title = {Poisson Hierarchy of Discrete Strings},
author = {Theodora Ioannidou and Antti Niemi},
journal= {arXiv preprint arXiv:1507.05792},
year = {2016}
}