nLab
quantization via the A-model

Context

Geometric quantization

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Contents

Idea

A method of quantization of mechanical systems represented by symplectic manifolds that produces the space of states of this system as the space of states of open strings in the A-model.

More in detail, the 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 coisotropic 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 at holographic principle for more on the general pattern.

The goal is to get closer to a systematic theory of quantization.

(Gukov-Witten 08, p.4)

References

The main original article is

Earlier, suggestions that the A-model is related to deformation quantization had been given in

which then have been extended and made more precise in

  • Vasily Pestun, Black hole entropy and topological strings on generalized CY manifolds, JHEP0609:034,2006 (arXiv:hep-th/0512189)

and in

in the context of generalized complex geometry.

Tha the space of states of open strings in the A-model can be interpreted as a quantization of the corresponding symplectic manifold had first been noticed in examples in

The canonical coisotropic brane was used to elucidate these matters further in

is the context of the Kapustin-Witten TQFT.

A relation to the path integral is discussed in

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

Revised on September 8, 2014 08:12:48 by David Corfield (129.12.18.225)