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Kähler structure in the commutative limit of matrix geometry

  • Goro IshikiEmail author
  • Takaki Matsumoto
  • Hisayoshi Muraki
Open Access
Regular Article - Theoretical Physics
First Online:

Abstract

We consider the commutative limit of matrix geometry described by a large-N sequence of some Hermitian matrices. Under some assumptions, we show that the commutative geometry possesses a Kähler structure. We find an explicit relation between the Kähler structure and the matrix configurations which define the matrix geometry. We also discuss a relation between the matrix configurations and those obtained from the geometric quantization.

Keywords

M(atrix) Theories Non-Commutative Geometry 
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Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Goro Ishiki
    • 1
    • 2
    Email author
  • Takaki Matsumoto
    • 2
  • Hisayoshi Muraki
    • 2
  1. 1.Center for Integrated Research in Fundamental Science and Engineering (CiRfSE)University of TsukubaTsukubaJapan
  2. 2.Graduate School of Pure and Applied SciencesUniversity of TsukubaTsukubaJapan

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