Poisson sigma models and deformation quantization

This is a review aimed at the physics audience on the relation between Poisson sigma models on surfaces with boundary and deformation quantization. These models are topological open string theories. In the classical Hamiltonian approach, we describe the reduced phase space and its structures (symplectic groupoid), explaining in particular the classical origin of the noncommutativity of the string endpoint coordinates. We also review the perturbative Lagrangian approach and its connection with Kontsevich's star product. Finally we comment on the relation between the two approaches.

talk: Villa Gualino 2000/10/02
sigma model: nonlinear
quantization: deformation
Hamiltonian formalism
charge: topological
group theory: geometrical
differential geometry: symplectic
string model

References(15)

Figures(0)

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Alberto S. Cattaneo
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Giovanni Felder
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- Zurich, ETH
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•
e-Print:
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•
DOI:
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Poisson sigma models and symplectic groupoids

Alberto S. Cattaneo
(
- Zurich U.
)
,
Giovanni Felder
(
- Zurich, ETH
)

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