scholarly journals Geometric prequantization of the moduli space of the vortex equations on a Riemann surface

2006 ◽  
Vol 47 (10) ◽  
pp. 103501 ◽  
Author(s):  
Rukmini Dey
Keyword(s):  
Riemann Surface ◽  
Moduli Space ◽  
Vortex Equations

scholarly journals QUANTIZATION OF A MODULI SPACE OF PARABOLIC HIGGS BUNDLES

2004 ◽  
Vol 15 (09) ◽  
pp. 907-917 ◽  
Author(s):  
INDRANIL BISWAS ◽  
AVIJIT MUKHERJEE
Keyword(s):  
Riemann Surface ◽  
Moduli Space ◽  
Symplectic Form ◽  
Dense Subset ◽  
Projective Structure ◽  
Open Dense Subset ◽  
Higgs Bundles ◽  
Smooth Variety ◽  
Structure Formula

Let [Formula: see text] be a moduli space of stable parabolic Higgs bundles of rank two over a Riemann surface X. It is a smooth variety defined over [Formula: see text] equipped with a holomorphic symplectic form. Fix a projective structure [Formula: see text] on X. Using [Formula: see text], we construct a quantization of a certain Zariski open dense subset of the symplectic variety [Formula: see text].

Moduli Space of Flat Connections as a Poisson Manifold

1997 ◽  
Vol 11 (26n27) ◽  
pp. 3195-3206 ◽  
Author(s):  
V. V. Fock ◽  
A. A. Rosly
Keyword(s):  
Riemann Surface ◽  
Lie Groups ◽  
Poisson Structure ◽  
Moduli Space ◽  
Poisson Manifold ◽  
Gauge Fields ◽  
Two Dimensional ◽  
Flat Connections ◽  
Lattice Gauge ◽  
Poisson Lie Groups

In this talk we describe the Poisson structure of the moduli space of flat connections on a two dimensional Riemann surface in terms of lattice gauge fields and Poisson–Lie groups.

scholarly journals The dimension of the Hilbert space of geometric quantization of vortices on a Riemann surface

2017 ◽  
Vol 14 (10) ◽  
pp. 1750144
Author(s):  
Rukmini Dey ◽  
Saibal Ganguli
Keyword(s):  
Hilbert Space ◽  
Riemann Surface ◽  
Line Bundle ◽  
Euler Characteristic ◽  
Moduli Space ◽  
Geometric Quantization

In this paper, we calculate the dimension of the Hilbert space of Kähler quantization of the moduli space of vortices on a Riemann surface. This dimension is given by the holomorphic Euler characteristic of the quantum line bundle.

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