منابع مشابه
Noncommutative Gravity
Various approaches by the author and collaborators to define gravitational fluctuations associated with a noncommutative space are reviewed. Geometry of a noncommutative space is defined by the data (A, H,D) where A is a noncommutative involutive algebra, H is a separable Hilbert space and D a self-adjoint operator on H referred to as Dirac operator [1]. Geometry on Riemannian manifolds could b...
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We study perturbative noncommutative quantum gravity by expanding the gravitational field about a fixed classical background. A calculation of the one loop gravitational self-energy graph reveals that only the non-planar graviton loops are damped by oscillating internal momentum dependent factors. The noncommutative quantum gravity perturbation theory is not renormalizable beyond one loop for m...
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We introduce the linear connection in the noncommutative geometry model of the product of continuous manifold and the discrete space of two points. We discuss its metric properties, de ne the metric connection and calculate the curvature. We de ne also the Ricci tensor and the scalar curvature. We nd that the latter di ers from the standard scalar curvature of the manifold by a term, which migh...
متن کاملLie algebraic Noncommutative Gravity
We exploit the Seiberg – Witten map technique to formulate the theory of gravity defined on a Lie algebraic noncommutative space time. Detailed expressions of the Seiberg – Witten maps for the gauge parameters, gauge potentials and the field strengths have been worked out. Our results demonstrate that notwithstanding the introduction of more general noncommutative structure there is no first or...
متن کاملNoncommutative Quantum Gravity
The possible role of gravity in a noncommutative geometry is investigated. Due to the Moyal *-product of fields in noncommutative geometry, it is necessary to complexify the metric tensor of gravity. We first consider the possibility of a complex Hermitian, nonsymmetric gμν and discuss the problems associated with such a theory. We then introduce a complex symmetric (non-Hermitian) metric, with...
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ژورنال
عنوان ژورنال: Physics of Particles and Nuclei Letters
سال: 2014
ISSN: 1547-4771,1531-8567
DOI: 10.1134/s1547477114070152