A New Solution to the Structure Equation in Noncommutative Spacetime

Nguyen Ai Viet
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Authors

  • Nguyen Ai Viet Information Technology Institute, Vietnam National Univeity

DOI:

https://doi.org/10.15625/0868-3166/24/1/3606

Keywords:

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

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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Published

12-03-2014

How to Cite

[1]
N. A. Viet, A New Solution to the Structure Equation in Noncommutative Spacetime, Comm. Phys. 24 (2014) 21. DOI: https://doi.org/10.15625/0868-3166/24/1/3606.

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Papers
Received 30-01-2014
Published 12-03-2014

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