Some special Kahler metrics on SL(2,C) and their holomorphic quantization
J. M. Baptista
Abstract
The group SU(2)*SU(2) acts naturally on SL(2,C) by simultaneous right and left multiplication. We study the Kahler metrics invariant under this action using global Kahler potentials. The volume growth and various curvature quantities are then explicitly computable. Examples include metrics of positive, negative and zero Ricci curvature, and the 1-lump metric of the CP1-model on a sphere. We then look at the holomorphic quantization of these metrics, where some physically satisfactory results on the dimension of the Hilbert space can be obtained. These give rise to an interesting geometrical conjecture, regarding the dimension of this space for general Stein manifolds in the semi-classical limit.
Create a lesson
Related papers
Phase transitions in non-Hermitian spherical integrals
Pierre Bousseyroux, Marc Potters
Factorization method for a clamped obstacle from near-field measurements via a far-field transformation
General Ozochiawaeze, Isaac Harris
Asymmetric phase transitions in random noncommutative geometries
Benedek Bukor, Masoud Khalkhali, Samuel Kováčik et al.
A Cumulative Framework for Solid Deformation
Lev Steinberg
Classification of pairs of second-order Hamiltonian operators and hydrodynamic type systems in six components
Giorgio Gubbiotti, Lambertus Van Geemen, Pierandrea Vergallo
Reconstructability of Inverse Problems under Symmetry: Separating Structural, Effective, and Physical Upper Bounds
Isshin Arai