Vol. 24 No. 1 (2014)
Papers

A New Solution to the Structure Equation in Noncommutative Spacetime

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  • Nguyen Ai Viet
Nguyen Ai Viet
Information Technology Institute, Vietnam National Univeity
DOI: https://doi.org/10.15625/0868-3166/24/1/3606

Published 12-03-2014

Keywords

  • non-commutative geometry,
  • gravity,
  • general relativity,
  • Kaluza-Klein theory,
  • Cartan formalism

How to Cite

Viet, N. A. (2014). A New Solution to the Structure Equation in Noncommutative Spacetime. Communications in Physics, 24(1), 21. https://doi.org/10.15625/0868-3166/24/1/3606
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Abstract

In this paper, starting from the common foundation of Connes' noncommutative geometry ( NCG)\cite{Connes1, Connes2, CoLo, Connes3}, various possible alternatives in the formulation of atheory of gravity in noncommutative spacetime are discussed indetails. The diversity in the final physical content of the theory is shown to be the consequence of the arbitrary choices in each construction steps. As an alternative in the last step, when the structure equations are to be solved, a minimal set of constraints on the torsion and connection is found to determine all the geometric notions in terms of the metric. In the Connes-Lott model of noncommutative spacetime, in order to keep the full spectrum of the discretized Kaluza-Klein theory \cite{VW2}, it is necessary to include the torsion in the generalized Einstein-Hilbert-Cartan action.
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