nLab
Kähler polarization

Context

Geometric quantization

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Symplectic geometry

Complex geometry

Contents

Idea

A polarization of a symplectic manifold induced by a compatible Kähler manifold structure.

𝒫T TX \mathcal{P} \subset T_{\mathbb{C}} T X
𝒫𝒫¯=0 \mathcal{P} \cap \overline{\mathcal{P}} = 0
𝒫={JvivvTX} \mathcal{P} = \left\{J v - i v \;|\; v \in T X \right\}

See also at

References

Discussion of the functoriality of Kähler polarization quantization with respect to the choice of metaplectically corrected Kähler structure is in section 3 of

  • Lauridsen, Aspects of quantum mathematics – Hitchin connections and the AJ conjecture, PhD thesis Aarhus 2010 (pdf)

Revised on July 17, 2013 21:05:25 by Urs Schreiber (82.169.65.155)