Noncommutative general relativity

Journal Article · Mon Aug 15 04:00:00 EDT 2005 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PhysRevD.72.045010· OSTI ID:20711374

Calmet, Xavier ^[1]; Kobakhidze, Archil ^[2]

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1. Service de Physique Theorique, Universite Libre de Bruxelles, CP225, Boulevard du Triomphe (Campus plaine), B-1050 Brussels (Belgium)
2. Department of Physics and Astronomy, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599 (United States)

We define a theory of noncommutative general relativity for canonical noncommutative spaces. We find a subclass of general coordinate transformations acting on canonical noncommutative spacetimes to be volume-preserving transformations. Local Lorentz invariance is treated as a gauge theory with the spin connection field taken in the so(3,1) enveloping algebra. The resulting theory appears to be a noncommutative extension of the unimodular theory of gravitation. We compute the leading order noncommutative correction to the action and derive the noncommutative correction to the equations of motion of the weak gravitation field.

• OSTI ID: 20711374
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 4 Vol. 72; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
COMMUTATION RELATIONS
COORDINATES
CORRECTIONS
EQUATIONS OF MOTION
GAUGE INVARIANCE
GENERAL RELATIVITY THEORY
GRAVITATION
LORENTZ INVARIANCE
QUANTUM FIELD THEORY
SO-3 GROUPS
SPACE-TIME
SPIN
TRANSFORMATIONS