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quantization via the A-model

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Context

Geometric quantization

geometric quantization higher geometric quantization

geometry of physics: Lagrangians and Action functionals + Geometric Quantization

Prerequisites

Prequantum field theiry

Geometric quantization

Theorems

Physics

physics, mathematical physics

Surveys, textbooks and lecture notes

theory (physics), model (physics)

Contents

Idea

A symplectic manifold serves as the target space for the 2-dimensional sigma-model TQFT called the A-model. If the symplectic manifold arises as the complexification of a phase space of some physical system, then one finds that the boundary path integral of the A-model on cosiotropic branes computes the path integral and the geometric quantization of this physical system.

The setup is reminiscent of how the deformation quantization of the phase space is computed by the 2-dimensional Poisson sigma-model. See holographic principle for more on the general pattern.

References

The main original article is

A relation to the path integral is discussed in

Relation to the B-model via mirror symmetry is discussed in

Revised on July 11, 2012 02:02:38 by Urs Schreiber (89.204.139.170)
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