Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Geometric quantization of the Hitchin system
View through CrossRef
This paper is about geometric quantization of the Hitchin system. We quantize a Kahler form on the Hitchin moduli space (which is half the first Kahler form defined by Hitchin) by considering the Quillen bundle as the prequantum line bundle and modifying the Quillen metric using the Higgs field so that the curvature is proportional to the Kahler form. We show that this Kahler form is integral and the Quillen bundle descends as a prequantum line bundle on the moduli space. It is holomorphic and hence one can take holomorphic square integrable sections as the Hilbert space of quantization of the Hitchin moduli space.
World Scientific Pub Co Pte Ltd
Title: Geometric quantization of the Hitchin system
Description:
This paper is about geometric quantization of the Hitchin system.
We quantize a Kahler form on the Hitchin moduli space (which is half the first Kahler form defined by Hitchin) by considering the Quillen bundle as the prequantum line bundle and modifying the Quillen metric using the Higgs field so that the curvature is proportional to the Kahler form.
We show that this Kahler form is integral and the Quillen bundle descends as a prequantum line bundle on the moduli space.
It is holomorphic and hence one can take holomorphic square integrable sections as the Hilbert space of quantization of the Hitchin moduli space.
Related Results
A Hitchin Connection for a Large Class of Families of Kähler Structures
A Hitchin Connection for a Large Class of Families of Kähler Structures
AbstractThis chapter presents a Hitchin connection constructed in a setting which significantly generalizes the setting covered by the first author, which, in turn, was a generaliz...
Constrained Quantization for Probability Distributions
Constrained Quantization for Probability Distributions
In this work, we extend the classical framework of quantization for Borel probability measures defined on normed spaces Rk by introducing and analyzing the notions of the nth const...
Mitigating Quantization Errors Due to Activation Spikes in Gated Linear Unit-Based Large Language Models
Mitigating Quantization Errors Due to Activation Spikes in Gated Linear Unit-Based Large Language Models
Modern large language models (LLMs) achieve state-of-the-art performance through architectural advancements but require high computational costs for inference. Post-training quanti...
Arithmetic constructions of thin representations in higher rank Teichmüller spaces
Arithmetic constructions of thin representations in higher rank Teichmüller spaces
Constructions arithmétiques de représentations fines dans les espaces de Teichmüller supérieurs
Dans cette thèse, nous construisons des sous-groupes de surface Zari...
Research on Quantization Parameter Decision Scheme for High Efficiency Video Coding
Research on Quantization Parameter Decision Scheme for High Efficiency Video Coding
High-Efficiency Video Coding (HEVC) is one of the most widely studied coding standards. It still uses the block-based hybrid coding framework of Advanced Video Coding (AVC), and co...
Quantization of the Quantum Hitchin System and the Real Geometric Langlands Correspondence
Quantization of the Quantum Hitchin System and the Real Geometric Langlands Correspondence
AbstractThis chapter proposes a natural quantization condition for the Hitchin system and relate this to the generating function for the variety of opers within the Hitchin space o...
Shrink and Eliminate: A Study of Post-Training Quantization and Repeated Operations Elimination in RNN Models
Shrink and Eliminate: A Study of Post-Training Quantization and Repeated Operations Elimination in RNN Models
Recurrent neural networks (RNNs) are neural networks (NN) designed for time-series applications. There is a growing interest in running RNNs to support these applications on edge d...
Valid Quantization: The Next Step
Valid Quantization: The Next Step
Canonical quantization is a wonderful procedure for selected problems, but there are many problems for which it fails. Affine quantization is a different procedure that has shown t...