Nonabelian Poisson Manifolds from D-Branes

Details Nonabelian Poisson Manifolds from D-Branes Nonabelian Poisson Manifolds from D-Branes

2004-07-27

arxiv.org/abs/hep-th/0407226v1

Mod.Phys.Lett. A19 (2004) 2541-2548

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

Superimposed D-branes have matrix-valued functions as their transverse coordinates, since the latter take values in the Lie algebra of the gauge group inside the stack of coincident branes. This leads to considering a classical dynamics where the multiplication law for coordinates and/or momenta, being given by matrix multiplication, is nonabelian. Quantisation further introduces noncommutativity as a deformation in powers of Planck's constant. Given an arbitrary simple Lie algebra and an arbitrary Poisson manifold, both finite-dimensional, we define a corresponding C*-algebra that can be regarded as a nonabelian Poisson manifold. The latter provides a natural framework for a matrix-valued classical dynamics.

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