Matrix geometry and coherent states

Goro Ishiki
Phys. Rev. D 92, 046009 – Published 31 August 2015

Abstract

We propose a novel method of finding the classical limit of the matrix geometry. We define coherent states for a general matrix geometry described by a large-N sequence of D Hermitian matrices Xμ(μ=1,2,,D) and construct a corresponding classical space as a set of all coherent states. When the classical space forms a smooth manifold, we also express various geometric objects on the classical space such as the metric, Levi-Civita connection, curvature and Poisson tensor, in terms of the matrix elements. This method provides a new class of observables in matrix models, which characterize geometric properties of matrix configurations.

  • Received 10 June 2015

DOI:https://doi.org/10.1103/PhysRevD.92.046009

© 2015 American Physical Society

Authors & Affiliations

Goro Ishiki*

  • Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan and Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan

  • *ishiki@het.ph.tsukuba.ac.jp

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Vol. 92, Iss. 4 — 15 August 2015

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