Volume 131, Number 2, July 2020
|Number of page(s)||6|
|Section||The Physics of Elementary Particles and Fields|
|Published online||07 August 2020|
A general relativity formulation for the Doplicher-Fredenhagen-Roberts noncommutative space-time
1 Department of Physics and Astronomy, University of Alabama - Tuscaloosa, AL 35487, USA
2 Departamento de Física, Universidade Federal Rural do Rio de Janeiro - BR 465-07, 23890-971, Seropédica, RJ, Brazil
3 Departamento de Física, Universidade Federal de Juiz de Fora - 36036-330, Juiz de Fora, MG, Brazil
4 Programa de Pós- Graduação Interdisciplinar em Física Aplicada, Instituto de Física, Universidade Federal do Rio de Janeiro - 21941-972, Rio de Janeiro, RJ, Brazil
Received: 3 May 2020
Accepted: 21 July 2020
The Doplicher, Fredenhagen and Roberts (DFR) noncommutative (NC) formalism was proposed in a curved space-time. In the DFR approach, the NC parameters are promoted to a set of space-time coordinates. Consequently, the field theory defined on this space contains extra dimensions. We propose a metric containing the new coordinates to explain the length measurements of this extended space. We promote the Minkowski part of this extended metric to a metric defined in a curved manifold. Thus, we can build up a NC gravitation model with extra dimensions. Based on the curved metric, we propose an Einstein-Hilbert action to describe the NC general relativity model on the DFR space. It is a new result in the literature since there is not a general relativity formalism in the DFR approach. We also introduce the NC version of the general relativistic field equations. As an application of the formalism, the weak-field approximation is considered in the field equations to generate the wave equations for the graviton propagation in DFR space.
PACS: 11.15.-q – Gauge field theories / 11.10.Ef – Lagrangian and Hamiltonian approach / 11.10.Nx – Noncommutative field theory
© 2020 EPLA
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.