JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2011, Vol. 46 ›› Issue (10): 1-31.

• Articles •     Next Articles

Noncommutative geometric approach to quantum spacetime

ZHANG Ruibin1, ZHANG Xiao2   

  1. 1. School of Mathematics and Statistics, University of Sydney, Sydney, Australia;
    2. Institute of Mathematics, Academy of Mathematics and Systems Science,
    Chinese Academy of Sciences, Beijing, China
  • Received:2011-07-12 Online:2011-10-20 Published:2011-10-18
  • About author:ZHANG Ruibin(1960- ), Male, Professor, his main research interests are in Lie theory and quantum physics. Email: rui.bin.zhang@sydney.edu.au ZHANG Xiao(1965- ), Male, Professor, his main research interests are in differential geometry, general relativity and noncommutative geometric. Email: xzhang@amss.ac.cn

Abstract:

Together with collaborators, we introduced a noncommutative Riemannian geometry over Moyal algebras and systematically developed it for noncommutative spaces embedded in higher dimensions in the last few years. The theory was applied to construct a noncommutative version of general relativity, which is expected to capture some essential structural features of spacetime at the Planck scale. Examples of noncommutative spacetimes were investigated in detail. These include quantisations of planefronted gravitational waves, quantum Schwarzschild spacetime and Schwarzschildde Sitterspacetime, and a quantum Tolman spacetime which is relevant to gravitational collapse. Here we briefly review the theory and its application in the study of quantum structure of spacetime.

Key words: noncommutative geometric, noncommutative general relativity, noncommutative Einstein field equation, Moyal algebras, quantum spacetime

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