8,205 research outputs found
On Poisson Structure and Curvature
We consider a curved space-time whose algebra of functions is the commutative
limit of a noncommutative algebra and which has therefore an induced Poisson
structure. In a simple example we determine a relation between this structure
and the Riemann tensor.Comment: 8 pages, Late
The classical r-matrix method for nonlinear sigma-model
The canonical Poisson structure of nonlinear sigma-model is presented as a
Lie-Poisson r-matrix bracket on coadjoint orbits. It is shown that the Poisson
structure of this model is determined by some `hidden singularities' of the Lax
matrix.Comment: 18 pages, LaTe
Poisson Structure Induced (Topological) Field Theories
A class of two dimensional field theories, based on (generically degenerate)
Poisson structures and generalizing gravity-Yang-Mills systems, is presented.
Locally, the solutions of the classical equations of motion are given. A
general scheme for the quantization of the models in a Hamiltonian formulation
is found.Comment: 6 pages, LaTeX, TUW940
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