724 research outputs found
Poisson sigma model and semiclassical quantization of integrable systems
In this paper we outline the construction of semiclassical eigenfunctions of
integrable models in terms of the semiclassical path integral for the Poisson
sigma model with the target space being the phase space of the integrable
system. The semiclassical path integral is defined as a formal power series
with coefficients being Feynman diagrams. We also argue that in a similar way
one can obtain irreducible semiclassical representations of Kontsevich's star
product.Comment: 22 pages, 12 figure
Lectures on Mirror Symmetry, Derived Categories, and D-branes
This paper is an introduction to Homological Mirror Symmetry, derived
categories, and topological D-branes aimed mainly at a mathematical audience.
In the paper we explain the physicists' viewpoint of the Mirror Phenomenon, its
relation to derived categories, and the reason why it is necessary to enlarge
the Fukaya category with coisotropic A-branes; we discuss how to extend the
definition of Floer homology to such objects and describe mirror symmetry for
flat tori. The paper consists of four lectures which were given at the
Institute for Pure and Applied Mathematics (Los Angeles), March 2003, as part
of a program on Symplectic Geometry and Physics.Comment: 30 page
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