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arXiv · 1004.2118

SL(2,C) gravity on noncommutative space with Poisson structure

Yan-Gang Miao·Shao-Jun Zhang
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Abstract

The Einstein's gravity theory can be formulated as an SL(2,C) gauge theory in terms of spinor notations. In this paper, we consider a noncommutative space with the Poisson structure and construct an SL(2,C) formulation of gravity on such a space. Using the covariant coordinate technique, we build a gauge invariant action in which, according to the Seiberg-Witten map, the physical degrees of freedom are expressed in terms of their commutative counterparts up to the first order in noncommutative parameters.

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Yan-Gang Miao, Shao-Jun Zhang. 2010-09-16. SL(2,C) gravity on noncommutative space with Poisson structure. https://doi.org/10.1103/physrevd.82.084017

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