Displaying similar documents to “Quantization of a dimensionally reduced Seiberg-Witten moduli space.”

Geometric quantization and no-go theorems

Viktor Ginzburg, Richard Montgomery (2000)

Banach Center Publications

Similarity:

A geometric quantization of a Kähler manifold, viewed as a symplectic manifold, depends on the complex structure compatible with the symplectic form. The quantizations form a vector bundle over the space of such complex structures. Having a canonical quantization would amount to finding a natural (projectively) flat connection on this vector bundle. We prove that for a broad class of manifolds, including symplectic homogeneous spaces (e.g., the sphere), such connection does not exist....

Determinant bundle over the universal moduli space of vector bundles over the Teichmüller space

Indranil Biswas (1997)

Annales de l'institut Fourier

Similarity:

The moduli space of stable vector bundles over a moving curve is constructed, and on this a generalized Weil-Petersson form is constructed. Using the local Riemann-Roch formula of Bismut-Gillet-Soulé it is shown that the generalized Weil-Petersson form is the curvature of the determinant line bundle, equipped with the Quillen metric, for a vector bundle on the fiber product of the universal moduli space with the universal curve.

Natural symplectic structures on the tangent bundle of a space-time

Janyška, Josef

Similarity:

In this nice paper the author proves that all natural symplectic forms on the tangent bundle of a pseudo-Riemannian manifold are pull-backs of the canonical symplectic form on the cotangent bundle with respect to some diffeomorphisms which are naturally induced by the metric.