Noncommutative Symmetries and Gravity

Abstract

Spacetime geometry is twisted (deformed) into noncommutative spacetime geometry, where functions and tensors are now star-multiplied. Consistently, spacetime diffeomorhisms are twisted into noncommutative diffeomorphisms. Their deformed Lie algebra structure and that of infinitesimal Poincare' transformations is defined and explicitly constructed. This allows to construct a noncommutative theory of gravity.

26 pages. Lectures given at the workshop `Noncommutative Geometry in Field and String Theories', Corfu Summer Institute on EPP, September 2005, Corfu, Greece. Version 2: Marie Curie European Reintegration Grant MERG-CT-2004-006374 acknowledged

References in corpus (9)

• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• A Gravity Theory on Noncommutative Spaces
• Noncommutative Geometry and Gravity
• Emergent Gravity from Noncommutative Gauge Theory
• New Lie-Algebraic and Quadratic Deformations of Minkowski Space from Twisted Poincare Symmetries
• Deformed Coordinate Spaces; Derivatives
• Construction of $\theta$-Poincaré Algebras and their Invariants on ${\mathcal{M}}_{\theta }$
• Gravity and the Structure of Noncommutative Algebras
• Space-time symmetry of noncommutative field theory

Cited by in corpus (26)

• Twisting all the way: from Classical Mechanics to Quantum Fields
• Noncommutative D=4 gravity coupled to fermions
• Noncommutative Gravity Solutions
• Twisted Noncommutative Field Theory with the Wick-Voros and Moyal Products
• Cosmological and Black Hole Spacetimes in Twisted Noncommutative Gravity
• Noncommutative field theory with the Wick-Voros product
• Noncommutative supergravity in D=3 and D=4
• Toward the classification of differential calculi on $\kappa$-Minkowski space and related field theories
• A unifying perspective on the Moyal and Voros products and their physical meanings
• Twisted Covariant Noncommutative Self-dual Gravity
• Wigner Oscillators, Twisted Hopf Algebras and Second Quantization
• Non-Commutative Geometry, Categories and Quantum Physics
• Symmetry Reduction in Twisted Noncommutative Gravity with Applications to Cosmology and Black Holes
• Field Theory on Nonanticommutative Superspace
• Non-commutative Quantum Mechanics in Three Dimensions and Rotational Symmetry
• Noncommutative oscillators from a Hopf algebra twist deformation. A first principles derivation
• Noncommutative Gravity and the *-Lie algebra of diffeomorphisms
• Canonical Noncommutativity Algebra for the Tetrad Field in General Relativity
• On Non-Commutative Correction of the Gödel-type Metric
• Star Product Geometries
• Twisted Supersymmetry in a Deformed Wess-Zumino Model in (2+1) Dimensions
• Energy momentum tensor for translation invariant renormalizable noncommutative field theory
• Symmetry Reduction and Exact Solutions in Twisted Noncommutative Gravity
• The Structure of Spacetime and Noncommutative Geometry
• A bigravity model from noncommutative geometry
• Hopf Algebras in Deformed Quantum Theories